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A descent algorithm FOR SOLVING MONOTONE VARIATIONAL-INEQUALITIES AND MONOTONE COMPLEMENTARITY-PROBLEMS

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1984年第3期44卷 485-496页

作者： SMITH, MJ Lecturer Department of Mathematics University of York Heslington York England

The paper provides a descent algorithm for solving certain monotone variational inequalities and shows how this algorithm may be used for solving certain monotone complementarity problems. Convergence is proved under ... 详细信息

关键词： Variational inequalities complementarity problems traffic equilibria monotonicity descent algorithm

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A descent algorithm-Based Parallel Variable Dual Matrix Model and Application to Blind Source Separation

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CIRCUITS SYSTEMS AND SIGNAL PROCESSING 2015年第1期34卷 269-300页

作者： Zeng, T. -J. Feng, Q. -Y. Southwest Jiaotong Univ Sch Informat Sci & Technol Chengdu Peoples R China

In this paper, we focus on the problem of blind source separation (BSS). To solve the problem efficiently, a new algorithm is proposed. First, a parallel variable dual-matrix model (PVDMM) that considers all the numerical relations between a mixing matrix and a separating matrix is proposed. Different constrained terms are used to construct the cost function for every sub-algorithm. These constrained terms reflect a numerical relation. Therefore, a number of undesired solutions are excluded, the search region is reduced, and the convergence efficiency of the algorithm is ultimately improved. Parallel sub-algorithms are proven to converge to a separable matrix only if the cost function approaches zero. Second, a descent algorithm (DA) as a PVDMM optimizing approach is proposed in this paper as well. Apparently, the efficiency of the algorithm depends completely on the DA. Unlike the traditional descent method, the DA defines step length by solving inequality instead of merely utilizing the Wolfe- or Armijo-type search rule. Stimulation results indicate that the DA can improve computational efficiency. Under mild conditions, the DA has been proven to have strong convergence properties. Numerical results also show that the method is very efficient and robust. Finally, we applied the combinative algorithm to the BSS problem. Computer simulations illustrate its good performance.

关键词： Blind source separation Joint diagonalization Parallel variable dual-matrix model descent algorithm

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A descent algorithm for generalized complementarity problems based on generalized Fischer-Burmeister functions

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COMPUTATIONAL & APPLIED MATHEMATICS 2018年第1期37卷 1-26页

作者： Tawhid, Mohamed A. Gu, Wei-Zhe Tran, Benjamin Thompson Rivers Univ Dept Math & Stat Fac Sci Kamloops BC V2C 0C8 Canada Alexandria Univ Dept Math & Comp Sci Fac Sci Alexandria 21511 Egypt Tianjin Univ Sch Sci Dept Math Tianjin 300072 Peoples R China

We study an unconstrained minimization approach to the generalized complementarity problem GCP(f, g) based on the generalized Fischer-Burmeister function and its generalizations when the underlying functions are . Also, we show how, under appropriate regularity conditions, minimizing the merit function corresponding to f and g leads to a solution of the generalized complementarity problem. Moreover, we propose a descent algorithm for GCP(f, g) and show a result on the global convergence of a descent algorithm for solving generalized complementarity problem. Finally, we present some preliminary numerical results. Our results further give a unified/generalization treatment of such results for the nonlinear complementarity problem based on generalized Fischer-Burmeister function and its generalizations.

关键词： Generalized complementarity problem GCP function Generalized FB function Unconstrained minimization Regularity conditions Merit function descent algorithm

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A NEW descent algorithm FOR SOLVING QUADRATIC BILEVEL PROGRAMMING PROBLEMS

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Acta Mathematicae Applicatae Sinica 2000年第3期16卷 235-244页

作者：韩继业刘国山汪寿阳 Institute of Applied Mathematics the Academy of Mathematics and Systems Sciences the Chinese Academy of Sciences Beijing China School of Business Administration Renmin University of China Beijing China Institute of Systems Science the Academy of Mathematics and Systems Science the Chinese Academy of Sciences Beijing China

In this paper, we give a descent algorithm for solving quadratic bilevel programming problems. It is proved that the descent algorithm finds a locally optimal solution to a quadratic bilevel programming problem in a ... 详细信息

关键词： Bilevel programming quadratic programming descent algorithm finite convergence

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Optimum design of planar steel frames under LRFD-AISC specifications using a step-by-step descent algorithm

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2022年第6期65卷 176-176页

作者： Sellami, Mohamed Univ Gabes Natl Engn Sch Gabes Res Unit Mechan Modeling Energy & Mat M2EM Gabes 6029 Tunisia Univ Gabes Natl Engn Sch Gabes Dept Civil Engn Gabes 6029 Tunisia

This paper presents a novel descent algorithm based on the step-by-step iterative principle, applied to the optimum design of steel frames. The search consists on finding the direction which decreases the structural weight most quickly. As the design problem includes discrete variables, the optimum is found by evaluating the structural weight gradient step by step. The step size is controlled in such a way that convergence towards infeasible or suboptimal solutions is avoided. By properly choosing the initial solution, it is possible to increase the efficiency and the convergence speed of the algorithm. Many strategies, for the choice of initial design point, by making use of engineering intuitions or using optimized design obtained by other algorithms are discussed. Furthermore, it is confirmed in this study that the proposed algorithm can be used to improve optimum designs found by metaheuristic algorithms. The optimization results, relative to several weight minimizations problems of benchmark planar steel frames designed according to Load and Resistance Factor Design, American Institute of Steel Construction (LRFD-AISC) specifications, are compared to those obtained by different optimization methods. The comparison proves the efficiency and robustness as well as the prompt of convergence of the proposed descent algorithm developed in this paper.

关键词： Optimum design of steel frames descent algorithm Gradient method Metaheuristic algorithms

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A NEW descent algorithm FOR THE LEAST ABSOLUTE VALUE REGRESSION PROBLEM

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COMMUNICATIONS IN STATISTICS PART B-SIMULATION AND COMPUTATION 1981年第5期10卷 479-491页

作者： WESOLOWSKY, GO McMaster University Hamilton Ontario Canada

This paper presents a new and simple algorithm for the least absolute value regression problem. It is based on the notion of “edge” descent along the surface of the objective function. It is comparable or better in computational efficiency to current linear programming approaches for roughly 4 or fewer independent variables. © 1981, Taylor & Francis Group, LLC. All rights reserved.

关键词： descent algorithm least absolute value regression

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The descent algorithms for Solving Symmetric Pareto Eigenvalue Complementarity Problem

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APPLICATIONS OF MATHEMATICS 2023年第4期68卷 441-465页

作者： Zou, Lu Lei, Yuan Hunan Univ Sch Math Lushan Rd S Changsha 410082 Peoples R China

For the symmetric Pareto Eigenvalue Complementarity Problem (EiCP), by reformulating it as a constrained optimization problem on a differentiable Rayleigh quotient function, we present a class of descent methods and prove their convergence. The main features include: using nonlinear complementarity functions (NCP functions) and Rayleigh quotient gradient as the descent direction, and determining the step size with exact linear search. In addition, these algorithms are further extended to solve the Generalized Eigenvalue Complementarity Problem (GEiCP) derived from unilateral friction elastic systems. Numerical experiments show the efficiency of the proposed methods compared to the projected steepest descent method with less CPU time.

关键词： Pareto eigenvalue complementarity problem generalized eigenvalue complementarity problem nonlinear complementarity function descent algorithm

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LOGNORMAL LAW FOR A RENORMALIZATION CHAIN ARISING IN SEARCH THEORY AND THE MODELING OF descent algorithmS

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OPERATIONS RESEARCH LETTERS 1986年第5期5卷 237-240页

作者： STEELE, JM Program in Engineering Statistics Princeton University Princeton NJ 08544 USA

A limit theorem is established for the asymptotic state of a Markov chain arising from an iterative renormalization. The limit theorem is illustrated in applications to the theory of random search and in probabilistic models for descent algorithms. Some special cases are also noted where exact distributional results can be obtained.

关键词： Markov chain lognormal descent algorithm

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A LINE SEARCH TECHNIQUE FOR descent algorithmS

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1982年第1期12卷 85-90页

作者： FATAH, MRA M.T.C Cairo Egypt

All descent algorithms are characterized by a line search step. For a convex minimized functional of a certain special form, a proposed line search process with definite and convenient estimation of the interval including the minimum point is given. In some cases this estimation is only an improvement of the initial point. A concrete example is tried using different descent algorithms. © 1982 Gordon and Breach Science Publishers Inc.

关键词： descent algorithm direct search Fibonacci golden section line search Unconstrained minimization

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A vectorial descent stepsize for parameter identification of a coupled parabolic PDE-ODE

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2015年第6期23卷 932-955页

作者： Kuate, Raphael Nassiopoulos, Alexandre Bourquin, Frederic Univ Paris Est IFSTTAR COSYS Paris France

We consider a simplified model of a coupled parabolic PDE-ODE describing heat transfer within buildings. We describe an identification procedure able to reconstruct the parameters of the model. The response of the model is nonlinear with respect to its parameters and the reconstruction of the parameters is achieved by the introduction of a new vectorial descent stepsize, which improves the convergence of the Levenberg-Marquardt minimization algorithm. The new vectorial descent stepsize can have negative and positive entries of different sizes, which fundamentally differs from standard scalar descent stepsize. The new algorithm is proved to converge and to outperform the standard scalar descent strategy. We also propose algorithms for the initialization of the parameters needed by the reconstruction procedure, when no a priori knowledge is available.

关键词： 35K05 65K10 93C20 35Q93 building energy performance optimization descent algorithm parameter identification inverse problems

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