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A NEWε-GENERALIZED PROJECTION METHOD OF strongLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED OPTIMIZATION

Journal of Systems Science & Complexity 2011年第3期24卷 604-618页

作者： Jinbao JIAN Guodong MA Chuanhao GUO College of Mathematics and Information Science Guangxi University Nanning 530004 China Department of Mathematics and Computer Science Yulin Normal University Yulin 537000 China College of Science Shanghai University Shanghai 200444 China.

In this paper, the nonlinear optimization problems with inequality constraints are discussed. Combining the ideas of the strongly sub-feasible directions method and the s-generalized projection technique, a new algorithm starting with an arbitrary initial iteration point for the discussed problems is presented. At each iteration, the search direction is generated by a new s-generalized projection explicit formula, and the step length is yielded by a new Armijo line search. Under some necessary assumptions, not only the algorithm possesses global and strong convergence, but also the iterative points always get into the feasible set after finite iterations. Finally, some preliminary numerical results are reported.

关键词： E-generalized projection global and strong convergence inequality constraints method of strongly sub-feasible directions optimization.

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A SSLE-TYPE ALGORITHM OF QUASI-strongLY SUB-FEASIBLE DIRECTIONS FOR INEQUALITY CONSTRAINED MINIMAX PROBLEMS

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Journal of Computational Mathematics 2023年第1期41卷 133-152页

作者： Jinbao Jian Guodong Ma Yufeng Zhang College of Mathematics and Physics Guangxi Key Laboratory of Hybrid Computation and IC Design AnalysisCenter for Applied Mathematics and Artificial IntelligenceGuangxi University for NationalitiesNanning 530006China School of Mathematics and Information Science Guangxi UniversityNanning 530004China

In this paper,we discuss the nonlinear minimax problems with inequality *** on the stationary conditions of the discussed problems,we propose a sequential systems of linear equations(SSLE)-type algorithm of quasi-strongly sub-feasible directions with an arbitrary initial iteration *** means of the new working set,we develop a new technique for constructing the sub-matrix in the lower right corner of the coefficient matrix of the system of linear equations(SLE).At each iteration,two systems of linear equations(SLEs)with the same uniformly nonsingular coefficient matrix are *** mild conditions,the proposed algorithm possesses global and strong ***,some preliminary numerical experiments are reported.

关键词： Inequality constraints Minimax problems Method of quasi-strongly subfeasible directions SSLE-type algorithm global and strong convergence

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