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Han, S. P.

Variable metric methods for minimizing a class of nondifferentiable functions. (English) Zbl 0441.90095

Math. Program. 20, 1-13 (1981).
Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page
scan of Zbl 0441.90095

Cited in 39 Documents

MSC:

90C30 Nonlinear programming
65K05 Numerical mathematical programming methods
41A25 Rate of convergence, degree of approximation
49J35 Existence of solutions for minimax problems

Keywords:

nondifferentiable function; stepsize procedure; nondifferentiable optimization; quasi-Newton methods; variable metric methods; minimax optimization; iterative solution of quadratic problems; global convergence
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\textit{S. P. Han}, Math. Program. 20, 1--13 (1981; Zbl 0441.90095)
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References:

[1] J.M. Danskin, ”The theory of max–min, with applications”,SIAM Journal on Applied Mathematics 14 (1966) 641–664. · Zbl 0144.43301
[2] V.F. Dem’yanov and V.N. Malozemov,Introduction to minimax (John Wiley & Sons, New York, 1974).
[3] J.E. Dennis Jr. and J.J. Moré, ”Quasi-Newton methods, motivation and theory”,SIAM Review 19 (1977) 46–89. · Zbl 0356.65041
[4] S.P. Han, ”Superlinearly convergent variable metric methods for general nonlinear programming”,Mathematical Programming 11 (1976) 263–282. · Zbl 0364.90097
[5] S.P. Han, ”Dual variable metric methods for constrained optimization”,SIAM Journal on Control and Optimization 15 (1977) 546–565. · Zbl 0361.90074
[6] S.P. Han, ”A global convergent method for nonlinear programming”,Journal of Optimization Theory and Applications 22 (1977) 297–309. · Zbl 0336.90046
[7] S.P. Han, ”A hybrid method of nonlinear programming”, in O.L. Mangasarian, R.R. Meyer and S.M. Robinson, Eds.,Nonlinear Programming 3 (Academic Press, New York, 1978) 65–95.
[8] S.P. Han, ”Superlinear convergence of a minimax method”, Cornell University, Computer Science TR78-336 (1978).
[9] C. Lemarechal, ”An extension of Davidon methods to nondifferentiable problems”,Mathematical Programming Study 3 (1975) 95–109.
[10] J.M. Ortega and W.C. Rheinboldt, Iterative solution of nonlinear equations in several variables (Academic Press, New York, 1970). · Zbl 0241.65046
[11] M.R. Osborne and G.A. Watson, ”An algorithm for minimax approximation in the nonlinear case”,Computer Journal 12 (1969) 64–69. · Zbl 0164.45802
[12] M.J.D. Powell, ”A fast algorithm for nonlinear constrained optimization calculations”, presented at the 1977 Dundee Conference on Numerical Analysis. · Zbl 0374.65032
[13] P. Wolfe, ”A method of conjugate subgradients for minimizing nondifferentiable functions”,Mathematical Programming Study 3 (1975) 145–173. · Zbl 0369.90093
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