Convergence of a dual algorithm for minimax problems

• Autorzy: He S-X. , Zhan L-W.
• Języki publikacji: EN

Abstrakty

EN

This paper studies the convergence of a dual algorithm for solving minimax problems proposed by Zhang and Tang (1997), which is based on a penalty function of Bertsekas (1982). It proves that the dual algorithm is locally convergent with linear convergence rate under the commonly used assumptions. Numerical results are presented to show the effectiveness of this algorithm.

Słowa kluczowe

EN

minimax problem; penalty function; dual algorithm; convergence

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2000
• Tom: Vol. 10, no. 1/2
• Strony: 47--60
• Opis fizyczny: Bibliogr. 12 poz., tab., wzory

Twórcy

autor

He S-X.

• Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 China

autor

Zhan L-W.

• Department of Applied Mathematics. Stale-Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

Bibliografia

• [1] B. P. Bertsekas: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, New York, 1982.
• [2] C. Charalambous: Nonliner least pth optimization and nonlinear programming. Math. Programming, 12 (1977), 195-225.
• [3] C. Charalambous: Acceleration of the least pth algorithm for minimax optimization with engineering applications. Math. Programming, 19 (1979), 270-297.
• [4] S.-P. Han and O. L. Mangasarian: Exact penalty function in nonlinear programming. Math. Programming, 17 (1979), 251-269.
• [5] X.-S. Li: An aggregate function method for nonlinear programming. Science in China (series A), 34:12 (1991), 1467-1473.
• [6] X.-S. Li: An entropy-based aggregate method for minimax optimization. Eng. Optim., 18(1992), 277-285.
• [7] X.-S. Li and S. C. Fang: On the entropic method for solving min-max problems with applications. Mathematical Methods of Operations Research, 46 (1997), 119-130.
• [8] R. A. Polyak: Smooth optimization methods for minimax problems. SIAM J. Control and Optimization, 26 (1988), 1274-1286.
• [9] H.-W. Tang and L.-W. Zhang: A maximum entropy method for linear programming. Chinese J. Num. Math. & Appli., 17:3 (1995), 54-65.
• [10] H.-W. Tang and L.-W Zhang: A maximum entropy method for convex programming. Chinese Science Bulletin, 40:5 (1995), 361-364.
• [11] A. B. Templeman and X.-S. Li: A maximum entropy approach to constrained nonlinear programming. Eng. Opt., 12 (1987), 191-205.
• [12] L.-W. Zhang and H.-W. Tang: A maximum entropy algorithm with parameters for solving minimax problem. Archives of Control Sciences, 6 (XLII) (1997), 47-59.