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CHARACTERIZING THE RATE OF CONVERGENCE OF THE AUGMENTED LAGRANGE METHOD FOR NONLINEAR PROGRAMMING 认领 引用
1
作者 Yule Zhang Jihong Zhang Jia Wu 《Journal of Computational Mathematics》 SCIE CSCD 2026年第6期1730-1748,共19页
The rate of convergence of the augmented Lagrangian method for solving nonlinear programming is studied under the Jacobian uniqueness conditions.It is demonstrated that,for a given multiplier vector(μ,λ),the rate of... The rate of convergence of the augmented Lagrangian method for solving nonlinear programming is studied under the Jacobian uniqueness conditions.It is demonstrated that,for a given multiplier vector(μ,λ),the rate of convergence of the augmented Lagrangian method is linear with respect to‖(μ,λ)-(μ*,λ*)‖and the ratio constant is proportional to 1/c when the ratio‖(μ,λ)-(μ*,λ*)‖/c is small enough,where c is the penalty parameter that exceeds a threshold c*>0 and(μ*,λ*)is the multiplier corresponding to a local minimum point.Importantly,the ratio constant of the Q-linear convergence of the sequence of multiplier vectors is estimated by the second-order derivative of the value function of the nonlinear optimization problem.This characterization gives an explicit expression for the rate constant of the Q-linear convergence of the sequence of multiplier vectors. 展开更多
关键词 Nonlinear Programming Jacobian Uniqueness Conditions Augmented Lagrangian Method Rate of Convergence Value Function
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Improved genetic algorithm for nonlinear programming problems 认领 引用 被引量：10
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作者 Kezong Tang Jingyu Yang +1 位作者 Haiyan Chen Shang Gao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2011年第3期540-546,共7页
An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector w... An improved genetic algorithm（IGA） based on a novel selection strategy to handle nonlinear programming problems is proposed.Each individual in selection process is represented as a three-dimensional feature vector which is composed of objective function value,the degree of constraints violations and the number of constraints violations.It is easy to distinguish excellent individuals from general individuals by using an individuals＇ feature vector.Additionally,a local search（LS） process is incorporated into selection operation so as to find feasible solutions located in the neighboring areas of some infeasible solutions.The combination of IGA and LS should offer the advantage of both the quality of solutions and diversity of solutions.Experimental results over a set of benchmark problems demonstrate that IGA has better performance than other algorithms. 展开更多
关键词 genetic algorithm（GA） nonlinear programming problem constraint handling non-dominated solution optimization problem.
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Further study on a class of augmented Lagrangians of Di Pillo and Grippo in nonlinear programming 认领 引用 被引量：2
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作者 杜学武 梁玉梅 张连生 《Journal of Shanghai University(English Edition)》 2006年第4期293-298,共6页
In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discus... In this paper, a class of augmented Lagrangiaus of Di Pillo and Grippo （DGALs） was considered, for solving equality-constrained problems via unconstrained minimization techniques. The relationship was further discussed between the uneonstrained minimizers of DGALs on the product space of problem variables and multipliers, and the solutions of the eonstrained problem and the corresponding values of the Lagrange multipliers. The resulting properties indicate more precisely that this class of DGALs is exact multiplier penalty functions. Therefore, a solution of the equslity-constralned problem and the corresponding values of the Lagrange multipliers can be found by performing a single unconstrained minimization of a DGAL on the product space of problem variables and multipliers. 展开更多
关键词 nonlinear programming constrained optimization augmented Lagrangians augmented Lagrangians of Di Pillo and Grippo.
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A Combined Homotopy Infeasible Interior-Point Method for Convex Nonlinear Programming 认领 引用 被引量：3
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作者 杨轶华 吕显瑞 刘庆怀 《Northeastern Mathematical Journal》 2006年第2期188-192,共5页
In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex n... In this paper, on the basis of the logarithmic barrier function and KKT conditions, we propose a combined homotopy infeasible interior-point method （CHIIP） for convex nonlinear programming problems. For any convex nonlinear programming, without strict convexity for the logarithmic barrier function, we get different solutions of the convex programming in different cases by CHIIP method. 展开更多
关键词 convex nonlinear programming infeasible interior point method homotopy method global convergence
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A Primal-dual Interior Point Method for Nonlinear Programming 认领 引用 被引量：1
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作者 张珊 姜志侠 《Northeastern Mathematical Journal》 2008年第3期275-282,共8页
In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local ... In this paper, we propose a primal-dual interior point method for solving general constrained nonlinear programming problems. To avoid the situation that the algorithm we use may converge to a saddle point or a local maximum, we utilize a merit function to guide the iterates toward a local minimum. Especially, we add the parameter ε to the Newton system when calculating the decrease directions. The global convergence is achieved by the decrease of a merit function. Furthermore, the numerical results confirm that the algorithm can solve this kind of problems in an efficient way. 展开更多
关键词 primal-dual interior point algorithm merit function global convergence nonlinear programming
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EXACT AUGMENTED LAGRANGIAN FUNCTION FOR NONLINEAR PROGRAMMING PROBLEMS WITH INEQUALITY CONSTRAINTS 认领 引用
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作者 杜学武 张连生 +1 位作者 尚有林 李铭明 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第12期1649-1656,共8页
An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstr... An exact augmented Lagrangian function for the nonlinear nonconvex programming problems with inequality constraints was discussed. Under suitable hypotheses, the relationship was established between the local unconstrained minimizers of the augmented Lagrangian function on the space of problem variables and the local minimizers of the original constrained problem. Furthermore, under some assumptions, the relationship was also established between the global solutions of the augmented Lagrangian function on some compact subset of the space of problem variables and the global solutions of the constrained problem. Therefore, f^om the theoretical point of view, a solution of the inequality constrained problem and the corresponding values of the Lagrange multipliers can be found by the well-known method of multipliers which resort to the unconstrained minimization of the augmented Lagrangian function presented. 展开更多
关键词 local minimizer global minimizer nonlinear programming exact penalty function augmented Lagrangian function
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A UNIVERSAL APPROACH FOR CONTINUOUS OR DISCRETE NONLINEAR PROGRAMMINGS WITH MULTIPLE VARIABLES AND CONSTRAINTS 认领 引用
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作者 孙焕纯 王跃芳 柴山 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2005年第10期1284-1292,共9页
A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with resp... A universal numerical approach for nonlinear mathematic programming problems is presented with an application of ratios of first-order differentials/differences of objective functions to constraint functions with respect to design variables. This approach can be efficiently used to solve continuous and, in particular, discrete programmings with arbitrary design variables and constraints. As a search method, this approach requires only computations of the functions and their partial derivatives or differences with respect to design variables, rather than any solution of mathematic equations. The present approach has been applied on many numerical examples as well as on some classical operational problems such as one-dimensional and two-dimensional knap-sack problems, one-dimensional and two-dimensional resource-distribution problems, problems of working reliability of composite systems and loading problems of machine, and more efficient and reliable solutions are obtained than traditional methods. The present approach can be used without limitation of modeling scales of the problem. Optimum solutions can be guaranteed as long as the objective function, constraint functions and their First-order derivatives/differences exist in the feasible domain or feasible set. There are no failures of convergence and instability when this approach is adopted. 展开更多
关键词 continuous or discrete nonlinear programming search algorithm relative differential/difference method
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Novel Method to Handle Inequality Constraints for Nonlinear Programming 认领 引用
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作者 黄远灿 《Journal of Beijing Institute of Technology》 EI CAS 2005年第2期145-149,共5页
By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constra... By redefining the multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, say, u2_i, i=1, 2, ..., m, nonnegative constraints imposed on inequality constraints in Karush-Kuhn-Tucker necessary conditions are removed. For constructing the Lagrange neural network and Lagrange multiplier method, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse those results dedicated to equality constraints, and they can be similarly proved with minor modification. Utilizing this technique, a new type of Lagrange neural network and a new type of Lagrange multiplier method are devised, which both handle inequality constraints directly. Also, their stability and convergence are analyzed rigorously. 展开更多
关键词 nonlinear programming inequality constraint Lagrange neural network Lagrange multiplier method convergence stability
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Penalized interior point approach for constrained nonlinear programming 认领 引用 被引量：1
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作者 陆文婷 姚奕荣 张连生 《Journal of Shanghai University(English Edition)》 2009年第3期248-254,共7页
A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal proble... A penalized interior point approach for constrained nonlinear programming is examined in this work. To overcome the difficulty of initialization for the interior point method, a problem equivalent to the primal problem via incorporating an auxiliary variable is constructed. A combined approach of logarithm barrier and quadratic penalty function is proposed to solve the problem. Based on Newton＇s method, the global convergence of interior point and line search algorithm is proven. Only a finite number of iterations is required to reach an approximate optimal solution. Numerical tests are given to show the effectiveness of the method. 展开更多
关键词 nonlinear programming interior point method barrier penalty function global convergence
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Nonlinear Programming Based Preamble Design for OFDM Systems 认领 引用
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作者 Ce-Wu Lu Xiao-Jun Liu +1 位作者 Yu-Jun Kuang Guang-You Fang 《Journal of Electronic Science and Technology of China》 2008年第1期25-28,共4页
A new preamble structure and design method for orthogonal frequency division multiplexing（OFDM）systems is described,which results a two-symbol long training preamble.The preamble contains four parts,the first part i... A new preamble structure and design method for orthogonal frequency division multiplexing（OFDM）systems is described,which results a two-symbol long training preamble.The preamble contains four parts,the first part is the same as the third,and the four parts are calculated by using nonlinear programming（NLP）model such that the moving correlation of the preamble results a steep rectangular-like pulse of certain width,whose step-down indicates the timing offset.Simulation results in AWGN channel are given to evaluate the perf o rmance of the proposed preamble design. 展开更多
关键词 Nonlinear programming orthogonal frequency division multiplexing preamble design symbolsynchronization.
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Nonlinear Programming Algorithm and Its Convergence Rate Analysis 认领 引用
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作者 Wang Guofu Li Xuequan 《Chinese Quarterly Journal of Mathematics》 1998年第1期8-13,共6页
In this paper,we improve the algorithm proposed by T.F.Colemen and A.R.Conn in paper[1].It is shown that the improved algorithm is possessed of global convergence and under some conditions it can obtain locally supper... In this paper,we improve the algorithm proposed by T.F.Colemen and A.R.Conn in paper[1].It is shown that the improved algorithm is possessed of global convergence and under some conditions it can obtain locally supperlinear convergence which is not possessed by the original algorithm. 展开更多
关键词 nonlinear programming exact penalty function algorithm
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NONLINEAR PROGRAMMING PROBLEMS IN MINE VENTILATION NETWORKS AND THEIR SOLUTIONS 认领 引用
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作者 Xie,Xian Ping Zhao,Zichwng Kunming Institute of Technology,Kunming 650093,China 《中国有色金属学会会刊：英文版》 1993年第2期88-91,96,共4页
Converting the balance equation of the branch of a mine ventilation network into an equivalent nonlinearprogramming problem,this paper proves that the total sum of the energy loss in every branch will be a minimumwhen... Converting the balance equation of the branch of a mine ventilation network into an equivalent nonlinearprogramming problem,this paper proves that the total sum of the energy loss in every branch will be a minimumwhen the airflow distribution in the networks is in a balanced state.The energy means of solving the networkequations by nodal methods is also noted,and a theorem for the unique existence of the solution for a networkbalance equation is give.An example is used to explain these conclusions. 展开更多
关键词 nonlinear programming mine ventilation energy airflow Distribution
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An overview of mathematical programming solvers:Theory,development,and recent advances 认领 引用
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作者 Lei HUANG Fan XIAO +2 位作者 Dongdong GE Wotao YIN Zhe LIANG 《ENGINEERING Management》 CSCD 2026年第1期1-16,共16页
Mathematical programming solvers are software tools designed to solve real‑world problems using mathematical programming algorithms.This survey explores the evolution of optimization technologies,from traditional meth... Mathematical programming solvers are software tools designed to solve real‑world problems using mathematical programming algorithms.This survey explores the evolution of optimization technologies,from traditional methods such as the simplex algorithm and branch‑and‑bound techniques to modern advancements that are facilitated by parallel computing,GPU acceleration,and AI algorithms.We also emphasize the recent emergence of mathematical programming solvers developed by research institutes and companies headquartered in China as major players,who have achieved remarkable success in benchmarks when compared to established solvers.This article provides a comprehensive overview of the theoretical foundations,historical progress,and emerging trends in mathematical programming solvers,offering valuable insights for both researchers and practitioners in the field. 展开更多
关键词 survey mathematical programming solver linear programming mixed‑integer programming nonlinear programming
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Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming 认领 引用 被引量：4
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作者 Vassilis M.Charitopoulos Lazaros G.Papageorgiou Vivek Dua 《Engineering》 SCIE EI CAS 2017年第2期202-213,共12页
In the present work,two new,(multi-)parametric programming(mp-P)-inspired algorithms for the solutionof mixed-integer nonlinear programming(MINLP)problems are developed,with their main focus being onprocess synthesis ... In the present work,two new,(multi-)parametric programming(mp-P)-inspired algorithms for the solutionof mixed-integer nonlinear programming(MINLP)problems are developed,with their main focus being onprocess synthesis problems.The algorithms are developed for the special case in which the nonlinearitiesarise because of logarithmic terms,with the first one being developed for the deterministic case,and thesecond for the parametric case(p-MINLP).The key idea is to formulate and solve the square system of thefirst-order Karush-Kuhn-Tucker(KKT)conditions in an analytical way,by treating the binary variables and/or uncertain parameters as symbolic parameters.To this effect,symbolic manipulation and solution tech-niques are employed.In order to demonstrate the applicability and validity of the proposed algorithms,twoprocess synthesis case studies are examined.The corresponding solutions are then validated using state-of-the-art numerical MINLP solvers.For p-MINLP,the solution is given by an optimal solution as an explicitfunction of the uncertain parameters. 展开更多
关键词 Parametric programming Uncertainty Process synthesis Mixed-integer nonlinear programming Symbolic manipulation
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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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A MULTIDIMENSIONAL FILTER SQP ALGORITHM FOR NONLINEAR PROGRAMMING 认领 引用 被引量：1
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作者 Wenjuan Xue Weiai Liu 《Journal of Computational Mathematics》 SCIE CSCD 2020年第5期683-704,共22页
We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the... We propose a multidimensional filter SQP algorithm.The multidimensional filter technique proposed by Gould et al.[SIAM J.Optim.,2005]is extended to solve constrained optimization problems.In our proposed algorithm,the constraints are partitioned into several parts,and the entry of our filter consists of these different parts.Not only the criteria for accepting a trial step would be relaxed,but the individual behavior of each part of constraints is considered.One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears.The other is that feasibility restoration phases are unnecessary because a consistent quadratic programming subproblem is used.We prove that our algorithm is globally convergent to KKT points under the constant positive generators(CPG)condition which is weaker than the well-known Mangasarian-Fromovitz constraint qualification(MFCQ)and the constant positive linear dependence(CPLD).Numerical results are presented to show the efficiency of the algorithm. 展开更多
关键词 Trust region Multidimensional filter Constant positive generators Global convergence Nonlinear programming
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A ROBUST TRUST REGION ALGORITHM FOR SOLVING GENERAL NONLINEAR PROGRAMMING 认领 引用 被引量：1
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作者 Xin-wei Liu Ya-xiang Yuan 《Journal of Computational Mathematics》 SCIE EI 2001年第3期309-322,共14页
Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N... Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; Numerical results of the study. 展开更多
关键词 trust region algorithm nonlinear programming
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NONLINEAR LAGRANGIANS FOR NONLINEAR PROGRAMMING BASED ON MODIFIED FISCHER-BURMEISTER NCP FUNCTIONS 认领 引用
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作者 Yonghong Ren Fangfang Guo Yang Li 《Journal of Computational Mathematics》 SCIE CSCD 2015年第4期396-414,共19页
This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of p... This paper proposes nonlinear Lagrangians based on modified Fischer-Burmeister NCP functions for solving nonlinear programming problems with inequality constraints. The convergence theorem shows that the sequence of points generated by this nonlinear La- grange algorithm is locally convergent when the penalty parameter is less than a threshold under a set of suitable conditions on problem functions, and the error bound of solution, depending on the penalty parameter, is also established. It is shown that the condition number of the nonlinear Lagrangian Hessian at the optimal solution is proportional to the controlling penalty parameter. Moreover, the paper develops the dual algorithm associ- ated with the proposed nonlinear Lagrangians. Numerical results reported suggest that the dual algorithm based on proposed nonlinear Lagrangians is effective for solving some nonlinear optimization problems. 展开更多
关键词 nonlinear Lagrangian nonlinear Programming modified Fischer-BurmeisterNCP function dual algorithm condition number
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A GENERAL TECHNIQUE FOR DEALING WITH DEGENERACY IN REDUCED GRADIENT METHODS FOR LINEARLY CONSTRAINED NONLINEAR PROGRAMMING 认领 引用
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作者 韩继业 胡晓东 《Acta Mathematicae Applicatae Sinica》 1994年第1期90-101,共12页
In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that t... In this paper we discuss the degeneracy in nonlinear programming with linear constraints, and give a technique for dealing with degeneracy in a general model of reduced gradient algorithms. Under the assumption that the objective function is continuously differentiable, we prove that either the iterative sequence {xk} generated by the method terminates at a Kuhn-Tucker point after a finite number of iterations, or any cluster point of the sequence {xk} is a KuhnTucker point. 展开更多
关键词 Degeneracy reduced gradient algorithms pivoting operation global convergence nonlinear programming
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GLOBAL CONVERGENCE AND IMPLEMENTATION OF NGTN METHOD FOR SOLVING LARGE-SCALE SMARSE NONLINEAR PROGRAMMING PROBLEMS 认领 引用
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作者 Qin Ni 《Journal of Computational Mathematics》 SCIE EI 2001年第4期337-346,共10页
An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable fo... An NGTN method was proposed for solving large-scale sparse nonlinear programming (NLP) problems. This is a hybrid method of a truncated Newton direction and a modified negative gradient direction, which is suitable for handling sparse data structure and pos sesses Q-quadratic convergence rate. The global convergence of this new method is proved, the convergence rate is further analysed, and the detailed implementation is discussed in this paper. Some numerical tests for solving truss optimization and large sparse problems are reported. The theoretical and numerical results show that the new method is efficient for solving large-scale sparse NLP problems. 展开更多
关键词 Nonlinear programming Large-scale problem Sparse.
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