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A feasible qp-free algorithm combining the interior-point method with active set for constrained optimization

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2009年第8期58卷 1520-1533页

作者： Jim, Jin-bao Quan, Ran Cheng, Wei-xin Guangxi Univ Coll Elect Engn Nanning 530004 Guangxi Peoples R China Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China Henan Normal Univ Coll Math & Informat Sci Xinxiang Peoples R China

In this paper, by means of "working set" technique for determining the active set and the idea of primal-dual interior-point method, a new feasible qp-free algorithm for solving inequality constrained optimization problems is presented. At each iteration, the algorithm solves only three reduced systems of linear equations with common coefficient matrix. Moreover, the initial iteration point can be at constraint boundary and the coefficient matrix is uniformly nonsingular without the strict complementarity. We also prove that the proposed algorithm obtains global and superlinear convergence. At last, preliminary numerical results are reported. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： qp-free algorithm Interior-point method Working set Global convergence Superlinear convergence

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A GLOBALLY CONVERGENT qp-free algorithm FOR INEQUALITY CONSTRAINED MINIMAX OPTIMIZATION

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Acta Mathematica Scientia 2020年第6期40卷 1723-1738页

作者： Jinbao JIAN Guodong MA College of Mathematics and Physics Guangxi University for NationalitiesNanning 530006China School of Mathematics and Statistics Yulin Normal UniversityYulin 537000China

Although qp-free algorithms have good theoretical convergence and are effective in practice,their applications to minimax optimization have not yet been *** this article,on the basis of the stationary conditions,without the exponential smooth function or constrained smooth transformation,we propose a qp-free algorithm for the nonlinear minimax optimization with inequality *** means of a new and much tighter working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient *** each iteration,to obtain the search direction,two reduced systems of linear equations with the same coefficient are *** mild conditions,the proposed algorithm is globally ***,some preliminary numerical experiments are reported,and these show that the algorithm is promising.

关键词： minimax optimization inequality constraints qp-free algorithm global convergence

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A qp-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization

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APPLIED MATHEMATICS AND COMPUTATION 2018年 316卷 52-72页

作者： Li, Jianling Yang, Zhenping Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China

In this paper, we present a qp-free algorithm without a penalty function or a filter for nonlinear general-constrained optimization. At each iteration, three systems of linear equations with the same coefficient matrix are solved to yield search direction;the nonmonotone line search ensures that the objective function or constraint violation function is sufficiently reduced. There is no feasibility restoration phase in our algorithm, which is necessary for filter methods. The algorithm possesses global convergence as well as superlinear convergence under some mild conditions including a weaker assumption of positive definiteness. Finally, some preliminary numerical results are reported. (C) 2017 Elsevier Inc. All rights reserved.

关键词： General-constrained optimization qp-free algorithm Penalty-function-free Filter-free Global convergence Superlinear convergence

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A superlinearly convergent qp-free algorithm for mathematical programs with equilibrium constraints

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APPLIED MATHEMATICS AND COMPUTATION 2015年 269卷 885-903页

作者： Li, Jianling Huang, Renshuai Jian, Jinbao Guangxi Univ Coll Math & Informat Sci Nanning 530004 Guangxi Peoples R China Yulin Normal Univ Coll Math & Informat Sci Yulin 537000 Guangxi Peoples R China

In this paper, based on the smoothing techniques and the working set techniques, a qp-free algorithm for mathematical programs with equilibrium constraints (MPEC for short) is presented. Firstly, by Fischer-Burmeister function and smoothing techniques, the discussed problem is approximated by a smooth constrained optimization problem. Secondly, the working set, which is used to construct systems of linear equations, is generated by pivoting operation. At each iteration, the search direction is yielded by solving two or three systems of equations with the same coefficient matrix. Under mild conditions, the global convergence and superlinear convergence are shown. Moreover, we can conclude that the current iterative point is an exact stationary point of the discussed problem if the proposed algorithm stops after finite iterations. Finally, preliminary numerical results are reported. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Equilibrium constraints Mathematical programs qp-free algorithm Global convergence Superlinear convergence

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A globally convergent qp-free algorithm for nonlinear semidefinite programming

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2017年第1期2017卷 145页

作者： Li, Jian-Ling Yang, Zhen-Ping Jian, Jin-Bao Guangxi Univ Coll Math & Informat Sci Daxue Rd 100 Nanning 530004 Guangxi Peoples R China Yulin Normal Univ Guangxi Coll & Univ Key Lab Complex Syst Optimiza Sch Math & Stat Jiaoyu Rd Yulin 537000 Guangxi Peoples R China

In this paper, we present a qp-free algorithm for nonlinear semidefinite programming. At each iteration, the search direction is yielded by solving two systems of linear equations with the same coefficient matrix;l(1) penalty function is used as merit function for line search, the step size is determined by Armijo type inexact line search. The global convergence of the proposed algorithm is shown under suitable conditions. Preliminary numerical results are reported.

关键词： nonlinear semidefinite programmming KKT conditions qp-free algorithm global convergence

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A global qp-free algorithm for mathematical programs with complementarity constraints

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2020年第1期2020卷 1-24页

作者： Li, Jian Ling Zhang, Qi Guangxi Univ Coll Math & Informat Sci Nanning Peoples R China

In this paper, a primal-dual interior point qp-free algorithm for mathematical programs with complementarity constraints is presented. Firstly, based on Fischer-Burmeister function and smoothing techniques, the investigated problem is approximated by a smooth nonlinear constrained optimization problem. Secondly, combining with an effective penalty function technique and working set, a qp-free algorithm is proposed to solve the smooth constrained optimization problem. At each iteration, only two reduced linear equations with the same coefficient matrix are solved to obtain the search direction. Under some mild conditions, the proposed algorithm possesses global convergence. Finally, some numerical results are reported.

关键词： Complementarity constraints Working set qp-free algorithm Global convergence

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The use of qp-free algorithm in the limit analysis of slope stability

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第13期235卷 3889-3897页

作者： Liu, Feng-Tao Fan, You-Hua Yin, Jian-Hua Shenzhen Grad Sch Harbin Inst Technol Shenzhen Peoples R China Hong Kong Polytech Univ Hong Kong Hong Kong Peoples R China

In many mountainous areas, landslides and slope instabilities frequently occur after heavy rainfall and earthquake, and result in enormous casualties and huge economic losses. In order to mitigate the landslides hazard efficiently, a method is required for a better understanding of stability analysis. Fortunately, upper bound theorem of limit analysis provides a practical and effective upper bound approach to evaluate the stability of slopes. And in this approach, the search for the minimum factor of safety can be formulated as a nonlinear constrained optimization. In general, the Sqp-type algorithms are used to solve this optimization problem. However, it is quite time consuming and difficult to search the optimum from an arbitrary starting point based on the Sqp-type algorithms. Fortunately, a qp-free algorithm based on penalty function and active-set strategy can be globally convergent toward the KKT points with arbitrary starting point, and the rate of convergence is local superlinear or even quadratic. Two classical problems of slope stability are solved by this qp-free algorithm. The results show that the qp-free algorithm would be the better choice than Sqp-type algorithms for solving the nonlinear constrained optimization problem which is derived from the upper bound limit analysis of slope stability. (C) 2011 Elsevier B.V. All rights reserved.

关键词： qp-free algorithm Slope stability Upper bound limit analysis

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The use of qp-free algorithm in the limit analysis of slope stability

The use of QP-free algorithm in the limit analysis of slope ...

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International Conference on Engineering and Computational Mathematics (ECM2009)

作者： Liu, Feng-Tao Fan, You-Hua Yin, Jian-Hua Shenzhen Grad Sch Harbin Inst Technol Shenzhen Peoples R China Hong Kong Polytech Univ Hong Kong Hong Kong Peoples R China

关键词： qp-free algorithm Slope stability Upper bound limit analysis

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A superlinearly convergent numerical algorithm for nonlinear programming

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NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 2012年第5期13卷 2391-2402页

作者： Zhu, Zhibin Wang, Shuo Guilin Univ Elect Technol Coll Math & Comp Sci Guilin 541004 Peoples R China

In this paper, a new algorithm is proposed to solve the nonlinear constrained optimization problems. Unlike sequential quadratic programming (Sqp) type methods, this algorithm does not involve solutions of quadratic programs. It is merely necessary to solve systems of linear equations with small scale to obtain a direction. The scheme is based on an idea of E-effective active set strategies. The theoretical analysis shows that global and superlinear convergence can be induced under some suitable conditions. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Inequality constrained optimization Sqp algorithm qp-free algorithm Global convergence Super linear convergence rate

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A globally and superlinearly convergent feasible qp-free method for nonlinear programming

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APPLIED MATHEMATICS AND COMPUTATION 2005年第1期168卷 519-539页

作者： Zhu, ZB Guilin Inst Elect Technol Dept Computat Sci & Math Guilin 541004 Peoples R China

In this paper, we propose a qp-free type algorithm which solves the problem of minimizing a smooth function subject to smooth inequality constraints. In contrast with the Sqp methods, each iteration this algorithm only needs to solve systems of linear equations which are derived from the equality part in the KKT first order optimality conditions. It is observed that, if the quasi-Newton direction is zero, we can obtain a direction of descent by dropping a constraint from the active set at the current iterate. A high order modified direction is introduced in order to prevent Maratos effect. Global and superlinear convergence are proven under some suitable conditions. (c) 2004 Elsevier Inc. All rights reserved.

关键词： constrained optimization qp-free algorithm Sqp algorithm system of linear equations global convergence superlinear convergence

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