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Entry trajectory optimization for cross-domain morphing vehicles by hybrid sequential second-order cone programming 认领 引用
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作者 Zheng Li Zhenyue Jia +2 位作者 Zheng Fang Hongmiao Zhou Jianqiao Yu 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2026年第4期149-175,共27页
This paper proposes a hybrid sequential second-order cone programming(HSSOCP)method with a three-layer scheme for the entry trajectory optimization of the cross-domain morphing vehicles(CDMVs).By defining the new morp... This paper proposes a hybrid sequential second-order cone programming(HSSOCP)method with a three-layer scheme for the entry trajectory optimization of the cross-domain morphing vehicles(CDMVs).By defining the new morphing rate control variable and using relaxation techniques to relax the bank angle constraint,the SOCP-based entry problem is constructed.A dynamic relaxation penal-ization technique is developed in the first layer to overcome artificial infeasibility and significantly enhance initialization robustness.A novel standard oscillation identification(SOI)method is proposed to precisely identify the iteration oscillations of basic SSOCP in the second layer,which can significantly improve the solution accuracy.A soft-trust-region strategy is applied in the third layer to eliminate oscillations and accelerate convergence.Simulation results of two scenarios demonstrate that the proposed SOI method effectively avoids non-standard oscillation interference versus traditional methods.The morphing aircraft can complete tasks better with a 7.01%and 10.43%reduction in heat load respectively compared to fixed-wing aircraft.The HSSOCP method can maintain accuracy while reducing computation time by 63.47%and 73.86%versus VATSSOCP.Monte Carlo simulations further validate the robustness. 展开更多
关键词 Cross-domain vehicle Morphing vehicle Entry trajectory optimization Sequential second-order cone programming Iteration oscillation Hybrid scheme
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Two new predictor-corrector algorithms for second-order cone programming 认领 引用 被引量：1
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作者 曾友芳 白延琴 +1 位作者 简金宝 唐春明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2011年第4期521-532,共12页
Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algor... Based on the ideas of infeasible interior-point methods and predictor-corrector algorithms, two interior-point predictor-corrector algorithms for the second-order cone programming （SOCP） are presented. The two algorithms use the Newton direction and the Euler direction as the predictor directions, respectively. The corrector directions belong to the category of the Alizadeh-Haeberly-Overton （AHO） directions. These algorithms are suitable to the cases of feasible and infeasible interior iterative points. A simpler neighborhood of the central path for the SOCP is proposed, which is the pivotal difference from other interior-point predictor-corrector algorithms. Under some assumptions, the algorithms possess the global, linear, and quadratic convergence. The complexity bound O（rln（εo/ε）） is obtained, where r denotes the number of the second-order cones in the SOCP problem. The numerical results show that the proposed algorithms are effective. 展开更多
关键词 second-order cone programming infeasible interior-point algorithm predictor-corrector algorithm global convergence complexity analysis
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Robust Blind Separation for MIMO Systems against Channel Mismatch Using Second-Order Cone Programming 认领 引用 被引量：1
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作者 Zhongqiang Luo Chengjie Li Lidong Zhu 《China Communications》 SCIE CSCD 2017年第6期168-178,共11页
To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple... To improve the deteriorated capacity gain and source recovery performance due to channel mismatch problem,this paper reports a research about blind separation method against channel mismatch in multiple-input multiple-output(MIMO) systems.The channel mismatch problem can be described as a channel with bounded fluctuant errors due to channel distortion or channel estimation errors.The problem of blind signal separation/extraction with channel mismatch is formulated as a cost function of blind source separation(BSS) subject to the second-order cone constraint,which can be called as second-order cone programing optimization problem.Then the resulting cost function is solved by approximate negentropy maximization using quasi-Newton iterative methods for blind separation/extraction source signals.Theoretical analysis demonstrates that the proposed algorithm has low computational complexity and improved performance advantages.Simulation results verify that the capacity gain and bit error rate(BER) performance of the proposed blind separation method is superior to those of the existing methods in MIMO systems with channel mismatch problem. 展开更多
关键词 multiple-input multiple-output channel mismatch second-order cone programming blind source separation independent component analysis
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Anti-interference beam pattern design based on second-order cone programming optimization 认领 引用 被引量：1
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作者 戴文舒 鲍凯凯 +1 位作者 王萍 王黎明 《Journal of Measurement Science and Instrumentation》 CAS CSCD 2016年第3期255-260,共6页
When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The ex... When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming. 展开更多
关键词 anti-interference beam pattern second-order cone programming optimization （SOCP） weak signal detection
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Improved design of reconfigurable frequency response masking filters based on second-order cone programming 认领 引用
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作者 吴尘 徐新洲 +1 位作者 黄程韦 赵力 《Journal of Southeast University(English Edition)》 EI CAS 2014年第4期422-427,共6页
In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that se... In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method. 展开更多
关键词 frequency response masking FRM filter optimal design reconfigurability second-order cone programming SOCP
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A VU-decomposition method for a second-order cone programming problem 认领 引用
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作者 陆媛 庞丽萍 夏尊铨 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2010年第2期263-270,共8页
A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential correspondi... A vu-decomposition method for solving a second-order cone problem is presented in this paper. It is first transformed into a nonlinear programming problem. Then, the structure of the Clarke subdifferential corresponding to the penalty function and some results of itsvu-decomposition are given. Under a certain condition, a twice continuously differentiable trajectory is computed to produce a second-order expansion of the objective function. A conceptual algorithm for solving this problem with a superlinear convergence rate is given. 展开更多
关键词 second-order cone programming nonsmooth optimization,vu-Lagrangian,vu-decomposition
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AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM 认领 引用 被引量：12
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作者 迟晓妮 刘三阳 《Acta Mathematica Scientia》 SCIE 2008年第3期551-559,共9页
A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorith... A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP. 展开更多
关键词 Second-order cone programming, infeasible-interior-point algorithm, predictor-corrector algorithm global convergence
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SMOOTHING NEWTON ALGORITHM FOR THE CIRCULAR CONE PROGRAMMING WITH A NONMONOTONE LINE SEARCH 认领 引用 被引量：8
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作者 迟晓妮 韦洪锦 +1 位作者 万仲平 朱志斌 《Acta Mathematica Scientia》 SCIE CSCD 2017年第5期1262-1280,共19页
In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space w... In this paper, we present a nonmonotone smoothing Newton algorithm for solving the circular cone programming(CCP) problem in which a linear function is minimized or maximized over the intersection of an affine space with the circular cone. Based on the relationship between the circular cone and the second-order cone(SOC), we reformulate the CCP problem as the second-order cone problem(SOCP). By extending the nonmonotone line search for unconstrained optimization to the CCP, a nonmonotone smoothing Newton method is proposed for solving the CCP. Under suitable assumptions, the proposed algorithm is shown to be globally and locally quadratically convergent. Some preliminary numerical results indicate the effectiveness of the proposed algorithm for solving the CCP. 展开更多
关键词 circular cone programming second-order cone programming nonmonotone line search smoothing Newton method local quadratic convergence
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Operational Coordination Optimization of Electricity and Natural Gas Networks Based on Sequential Symmetrical Second-order Cone Programming 认领 引用
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作者 Liang Min Chengwei Lou +2 位作者 Jin Yang James Yu Zhibin Yu 《Journal of Modern Power Systems and Clean Energy》 SCIE EI CSCD 2025年第2期488-499,共12页
The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distr... The variable and unpredictable nature of renewable energy generation(REG)presents challenges to its large-scale integration and the efficient and economic operation of the electricity network,particularly at the distribution level.In this paper,an operational coordination optimization method is proposed for the electricity and natural gas networks,aiming to overcome the identified negative impacts.The method involves the implementation of bi-directional energy flows through power-to-gas units and gas-fired power plants.A detailed model of the three-phase power distribution system up to each phase is employed to improve the representation of multi-energy systems to consider real-world end-user consumption.This method allows for the full consideration of unbalanced operational scenarios.Meanwhile,the natural gas network is modelled and analyzed with steady-state gas flows and the dynamics of the line pack in pipelines.The sequential symmetrical second-order cone programming(SS-SOCP)method is employed to facilitate the simultaneous analysis of three-phase imbalance and line pack while accelerating the solution process.The efficacy of the operational coordination optimization method is demonstrated in case studies comprising a modified IEEE 123-node power distribution system with a 20-node natural gas network.The studies show that the operational coordination optimization method can simultaneously minimize the total operational cost,the curtailment of installed REG,the voltage imbalance of three-phase power system,and the overall carbon emissions. 展开更多
关键词 Operational coordination multi-energy system power-to-gas electricity network natural gas network second-order cone programming
Multiple-constraint cooperative guidance based on two-stage sequential convex programming 认领 引用 被引量：20
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作者 Wei DONG Qiuqiu WEN +1 位作者 Qunli XIA Shengjiang YANG 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2020年第1期296-307,共12页
An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a... An improved approach is presented in this paper to implement highly constrained cooperative guidance to attack a stationary target.The problem with time-varying Proportional Navigation(PN)gain is first formulated as a nonlinear optimal control problem,which is difficult to solve due to the existence of nonlinear kinematics and nonconvex constraints.After convexification treatments and discretization,the solution to the original problem can be approximately obtained by solving a sequence of Second-Order Cone Programming(SOCP)problems,which can be readily solved by state-of-the-art Interior-Point Methods(IPMs).To mitigate the sensibility of the algorithm on the user-provided initial profile,a Two-Stage Sequential Convex Programming(TSSCP)method is presented in detail.Furthermore,numerical simulations under different mission scenarios are conducted to show the superiority of the proposed method in solving the cooperative guidance problem.The research indicated that the TSSCP method is more tractable and reliable than the traditional methods and has great potential for real-time processing and on-board implementation. 展开更多
关键词 Convex optimization Cooperative guidance Guidance Multiple constraints Second-order cone programming Sequential convex programming
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Day-ahead Optimization Schedule for Gas-electric Integrated Energy System Based on Second-order Cone Programming 认领 引用 被引量：33
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作者 Yonghui Sun Bowen Zhang +3 位作者 Leijiao Ge Denis Sidorov Jianxi Wang Zhou Xu 《CSEE Journal of Power and Energy Systems》 SCIE EI CSCD 2020年第1期142-151,共10页
This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas sy... This paper proposes an optimal day-ahead opti-mization schedule for gas-electric integrated energy system(IES)considering the bi-directional energy flow.The hourly topology of electric power system(EPS),natural gas system(NGS),energy hubs(EH)integrated power to gas(P2G)unit,are modeled to minimize the day-ahead operation cost of IES.Then,a second-order cone programming(SOCP)method is utilized to solve the optimization problem,which is actually a mixed integer nonconvex and nonlinear programming issue.Besides,cutting planes are added to ensure the exactness of the global optimal solution.Finally,simulation results demonstrate that the proposed optimization schedule can provide a safe,effective and economical day-ahead scheduling scheme for gas-electric IES. 展开更多
关键词 Day-ahead optimization schedule integrated energy system natural gas system second-order cone programming
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Exact Computable Representation of Some Second-Order Cone Constrained Quadratic Programming Problems 认领 引用 被引量：2
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作者 Qingwei Jin Ye Tian +2 位作者 Zhibin Deng Shu-Cherng Fang Wenxun Xing 《Journal of the Operations Research Society of China》 EI 2013年第1期107-134,共28页
Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a noncon... Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints. 展开更多
关键词 Linear conic program Semidefinite program Nonconvex quadratically constrained quadratic program Second-order cone
Optimal design and verification of temporal and spatial filters using second-order cone programming approach 认领 引用 被引量：8
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作者 YAN Shefeng MA Yuanliang 《Science in China(Series F)》 2006年第2期235-253,共19页
Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also... Temporal filters and spatial filters are widely used in many areas of signal processing. A number of optimal design criteria to these problems are available in the literature. Various computational techniques are also presented to optimize these criteria chosen. There are many drawbacks in these methods. In this paper, we introduce a unified framework for optimal design of temporal and spatial filters. Most of the optimal design problems of FIR filters and beamformers are included in the framework. It is shown that all the design problems can be reformulated as convex optimization form as the second-order cone programming （SOCP） and solved efficiently via the well-established interior point methods. The main advantage of our SOCP approach as compared with earlier approaches is that it can include most of the existing methods as its special cases, which leads to more flexible designs. Furthermore, the SOCP approach can optimize multiple required performance measures, which is the drawback of earlier approaches. The SOCP approach is also developed to optimally design temporal and spatial two-dimensional filter and spatial matrix filter. Numerical results demonstrate the effectiveness of the proposed approach. 展开更多
关键词 filter design beamformer design spatial filter design second-order cone programming.
Nonsingularity in second-order cone programming via the smoothing metric projector 认领 引用 被引量：2
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作者 WANG Yun ZHANG LiWei 《Science China Mathematics》 SCIE 2010年第4期1025-1038,共14页
Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of... Based on the differential properties of the smoothing metric projector onto the second-order cone,we prove that,for a locally optimal solution to a nonlinear second-order cone programming problem,the nonsingularity of the Clarke's generalized Jacobian of the smoothing Karush-Kuhn-Tucker system,constructed by the smoothing metric projector,is equivalent to the strong second-order sufficient condition and constraint nondegeneracy,which is in turn equivalent to the strong regularity of the Karush-Kuhn-Tucker point.Moreover,this nonsingularity property guarantees the quadratic convergence of the corresponding smoothing Newton method for solving a Karush-Kuhn-Tucker point.Interestingly,the analysis does not need the strict complementarity condition. 展开更多
关键词 second-order cone programming problem smoothing metric projector B-subdifferential Clarke’s generalized Jacobian smoothing Newton method
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Unified convergence analysis of a second-order method of multipliers for nonlinear conic programming 认领 引用
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作者 Liang Chen Junyuan Zhu Xinyuan Zhao 《Science China Mathematics》 SCIE CSCD 2022年第11期2397-2422,共26页
In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.S... In this paper,we accomplish the unified convergence analysis of a second-order method of multipliers(i.e.,a second-order augmented Lagrangian method)for solving the conventional nonlinear conic optimization problems.Specifically,the algorithm that we investigate incorporates a specially designed nonsmooth(generalized)Newton step to furnish a second-order update rule for the multipliers.We first show in a unified fashion that under a few abstract assumptions,the proposed method is locally convergent and possesses a(nonasymptotic)superlinear convergence rate,even though the penalty parameter is fixed and/or the strict complementarity fails.Subsequently,we demonstrate that for the three typical scenarios,i.e.,the classic nonlinear programming,the nonlinear second-order cone programming and the nonlinear semidefinite programming,these abstract assumptions are nothing but exactly the implications of the iconic sufficient conditions that are assumed for establishing the Q-linear convergence rates of the method of multipliers without assuming the strict complementarity. 展开更多
关键词 second-order method of multipliers augmented Lagrangian method convergence rate generalized Newton method second-order cone programming semidefinite programming
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Pre-filters design for weighted sum rate maximization in multiuser time reversal downlink systems 认领 引用
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作者 Mingyue Wang Fangwei Li +1 位作者 Yingsong Li Shengyuan Luo 《Digital Communications and Networks》 SCIE EI CSCD 2025年第6期1908-1916,共9页
In high-speed multiuser Time Reversal(TR)downlink systems,the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference.Moreover,maximizing the weighted sum rate in such syst... In high-speed multiuser Time Reversal(TR)downlink systems,the transmission rate is degraded due to the presence of severe inter-user and inter-symbol interference.Moreover,maximizing the weighted sum rate in such systems is a critical objective,since the weighting factors represent the priority of different users in different applications.However,it faces significant challenges as it is an NP-hard and non-convex problem.In order to suppress these interferences and maximize the weighted sum rate,in this paper we present a novel approach for the joint design of the pre-filters.The proposed method applies successive convex approximation to transform the original problem into a Second-Order Cone Programming(SOCP)problem.Then,a low-complexity iterative algorithm is provided to effectively solve the resulting SOCP problem.According to the simulation results,the proposed method reaches a local optimum within a few iterations and demonstrates superior performance in terms of weighted sum rate compared to the current algorithm. 展开更多
关键词 Pre-filters design Successive convex approximation Second-order cone programming Time reversal Weighted sum rate
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Quadratic Optimization over a Second-Order Cone with Linear Equality Constraints 认领 引用 被引量：1
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作者 Xiao-ling Guo Zhi-bin Deng +2 位作者 Shu-Cherng Fang Zhen-bo Wang Wen-xun Xing 《Journal of the Operations Research Society of China》 EI 2014年第1期17-38,共22页
This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be ... This paper studies the nonhomogeneous quadratic programming problem over a second-order cone with linear equality constraints.When the feasible region is bounded,we show that an optimal solution of the problem can be found in polynomial time.When the feasible region is unbounded,a semidefinite programming(SDP)reformulation is constructed to find the optimal objective value of the original problem in polynomial time.In addition,we provide two sufficient conditions,under which,if the optimal objective value is finite,we show the optimal solution of SDP reformulation can be decomposed into the original space to generate an optimal solution of the original problem in polynomial time.Otherwise,a recession direction can be identified in polynomial time.Numerical examples are included to illustrate the effectiveness of the proposed approach. 展开更多
关键词 Quadratic programming Linear conic programming Second-order cone Cone of nonnegative quadratic functions
Multiconstraint adaptive three-dimensional guidance law using convex optimization 认领 引用 被引量：7
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作者 FU Shengnan LIU Xiaodong +1 位作者 ZHANG Wenjie XIA Qunli 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2020年第4期791-803,共13页
The traditional guidance law only guarantees the accuracy of attacking a target.However,the look angle and acceleration constraints are indispensable in applications.A new adaptive three-dimensional proportional navig... The traditional guidance law only guarantees the accuracy of attacking a target.However,the look angle and acceleration constraints are indispensable in applications.A new adaptive three-dimensional proportional navigation(PN)guidance law is proposed based on convex optimization.Decomposition of the three-dimensional space is carried out to establish threedimensional kinematic engagements.The constraints and the performance index are disposed by using the convex optimization method.PN guidance gains can be obtained by solving the optimization problem.This solution is more rapid and programmatic than the traditional method and provides a foundation for future online guidance methods,which is of great value for engineering applications. 展开更多
关键词 proportional navigation(PN) adaptive guidance law three-dimensional space second-order cone programming(SOCP) convex optimal control
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Strain localization of Mohr-Coulomb soils with non-associated plasticity based on micropolar continuum theory 认领 引用 被引量：4
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作者 Jianbin Tang Xi Chen +1 位作者 Liusheng Cui Zongqi Liu 《Journal of Rock Mechanics and Geotechnical Engineering》 SCIE CSCD 2023年第12期3316-3327,共12页
To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the ... To address the problems of strain localization, the exact Mohr-Coulomb (MC) model is used based on second-order cone programming (mpcFEM-SOCP) in the framework of micropolar continuum finite element method. Using the uniaxial compression test, we focused on the earth pressure problem of rigid wall segment involving non-associated plasticity. The numerical results reveal that when mpcFEM-SOCP is applied, the problems of mesh dependency can be effectively addressed. For geotechnical strain localization analysis involving non-associated MC plasticity, mpcFEM-SOCP in conjunction with the pseudo-time discrete scheme can improve the numerical stability and avoid the unreasonable softening issue in the pressure-displacement curves, which may be encountered in the conventional FEM. It also shows that the pressure-displacement responses calculated by mpcFEM-SOCP with the pseudo-time discrete scheme are higher than those calculated by mpcFEM-SOCP with the Davis scheme. The inclination angle of shear band predicted by mpcFEM-SOCP with the pseudo-time discrete scheme agrees well with the theoretical solution of non-associated MC plasticity. 展开更多
关键词 Strain localization Micropolar continuum Mohr-Coulomb(MC)model Non-associated plasticity Second-order cone programming
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Optimality conditions for sparse nonlinear programming 认领 引用 被引量：9
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作者 PAN LiLi XIU NaiHua FAN Jun 《Science China Mathematics》 SCIE CSCD 2017年第5期759-776,共18页
The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qu... The sparse nonlinear programming （SNP） is to minimize a general continuously differentiable func- tion subject to sparsity, nonlinear equality and inequality constraints. We first define two restricted constraint qualifications and show how these constraint qualifications can be applied to obtain the decomposition properties of the Frechet, Mordukhovich and Clarke normal cones to the sparsity constrained feasible set. Based on the decomposition properties of the normal cones, we then present and analyze three classes of Karush-Kuhn- Tucker （KKT） conditions for the SNP. At last, we establish the second-order necessary optimality condition and sufficient optimality condition for the SNP. 展开更多
关键词 sparse nonlinear programming constraint qualification normal cone first-order optimality con-dition second-order optimality condition
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