A sequential quadratic programming algorithm for nonlinear minimax problems

Hu, Quan; Hu, J. Y.

doi:10.1017/s0004972700039745

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…The extraordinary efficiency of SQP methods in solving nonlinear constrained optimization problems (NLP) has allowed its extension to many other problems, such as minimax problems [8][9][10][11][12][13]. But the sequences may fail to converge as the initial point lies far from the optimal point in the SQP algorithm.…”

Section: Introductionmentioning

confidence: 99%

The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization

Su¹,

Liu²,

Lu³

2023

PLoS ONE

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In this paper, we proposed an adaptive QP-free method without a penalty function or a filter for minimax optimization. In each iteration, solved two linear systems of equations constructed from Lagrange multipliers and KKT-conditioned NCP functions. Based on the work set, the computational scale is further reduced. Instead of the filter structure, we adopt a nonmonotonic equilibrium mechanism with an adaptive parameter adjusted according to the result of each iteration. Feasibility of the algorithm are given, and the convergence under some assumptions is demonstrated. Numerical results and practical application are reported at the end.

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Section: Introductionmentioning

confidence: 99%

The global convergence properties of an adaptive QP-free method without a penalty function or a filter for minimax optimization

Su¹,

Liu²,

Lu³

2023

PLoS ONE

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“…Hu and J.-Z. Hu [ 23 ] process pivoting operation to generate an ɛ -active constraint subset associated with the current iteration point. At each iteration of their proposed algorithm, a main search direction is obtained by solving a reduced quadratic program which always has a solution.…”

Section: Introductionmentioning

confidence: 99%

A Simple SQP Algorithm for Constrained Finite Minimax Problems

Wang

Luo

2014

The Scientific World Journal

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A simple sequential quadratic programming method is proposed to solve the constrained minimax problem. At each iteration, through introducing an auxiliary variable, the descent direction is given by solving only one quadratic programming. By solving a corresponding quadratic programming, a high-order revised direction is obtained, which can avoid the Maratos effect. Furthermore, under some mild conditions, the global and superlinear convergence of the algorithm is achieved. Finally, some numerical results reported show that the algorithm in this paper is successful.

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