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多目标0-1线性规划的交互式算法 认领 引用 被引量：3
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作者 孙艳丰 《北方交通大学学报》 北大核心 1994年第4期464-468,共5页
提出一个求解多目标0－1线性规划问题的交互式算法，并分析了该算法的特点，即有很强的搜索功能和很宽的适用范围，最后将此算法用于实际，得到了满意的结果。
关键词 多目标规划 0-1规划 线性规划 交互式算法
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1-Bit compressive sensing: Reformulation and RRSP-based sign recovery theory 认领 引用 被引量：5
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作者 ZHAO YunBin XU ChunLei 《Science China Mathematics》 SCIE CSCD 2016年第10期2049-2074,共26页
Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or ... Recently, the 1-bit compressive sensing （1-bit CS） has been studied in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit CS is not available, it is often the support or the sign of a signal that can be exactly recovered with a decoding method. We first show that a necessary assumption （that has been overlooked in the literature） should be made for some existing theories and discussions for 1-bit CS. Without such an assumption, the found solution by some existing decoding algorithms might be inconsistent with 1-bit measurements. This motivates us to pursue a new direction to develop uniform and nonuniform recovery theories for 1-bit CS with a new decoding method which always generates a solution consistent with 1-bit measurements. We focus on an extreme case of 1-bit CS, in which the measurements capture only the sign of the product of a sensing matrix and a signal. We show that the 1-bit CS model can be reformulated equivalently as an t0-minimization problem with linear constraints. This reformulation naturally leads to a new linear-program-based decoding method, referred to as the 1-bit basis pursuit, which is remarkably different from existing formulations. It turns out that the uniqueness condition for the solution of the 1-bit basis pursuit yields the so-called restricted range space property （RRSP） of the transposed sensing matrix. This concept provides a basis to develop sign recovery conditions for sparse signals through 1-bit measurements. We prove that if the sign of a sparse signal can be exactly recovered from 1-bit measurements with 1-bit basis pursuit, then the sensing matrix must admit a certain RRSP, and that if the sensing matrix admits a slightly enhanced RRSP, then the sign of a k-sparse signal can be exactly recovered with 1-bit basis pursuit. 展开更多
关键词 1-bit compressive sensing restricted range space property 1-bit basis pursuit linear program,l0-minimization sparse signal recovery
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A New Sparse Recovery Method for the Inverse Acoustic Scattering Problem 认领 引用
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作者 Chang-long WANG Jun-xiong JIA +1 位作者 Ji-gen PENG Shou-jin LIN 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2020年第1期49-66,共18页
Based on sparse information recovery,we develop a new method for locating multiple multiscale acoustic scatterers.Firstly,with the prior information of the scatterers’shape,we reformulate the location identification ... Based on sparse information recovery,we develop a new method for locating multiple multiscale acoustic scatterers.Firstly,with the prior information of the scatterers’shape,we reformulate the location identification problem into a sparse information recovery model which brought the power of sparse recovery method into this type of inverse scattering problems.Specifically,the new model can advance the judgment of the existence of alternative scatterers and,in the meantime,conclude the number and locating of each existing scatterers.Secondly,as well known,the core model(l0-minimization)in sparse information recovery is an NP-hard problem.According to the characteristics of the proposed sparse model,we present a new substitute method and give a detailed theoretical analysis of the new substitute model.Relying on the properties of the new model,we construct a basic algorithm and an improved one.Finally,we verify the validity of the proposed method through two numerical experiments. 展开更多
关键词 sparse recovery acoustic scatterer l0-minimization substitute function
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