Numerical Methods for Minimizing Quasidifferentiable Functions: A Survey and Comparison

This paper presents a survey of some numerical algorithms for solving the problem of unconstrained minimization of a large class of quasidifferentiable functions. We report the results of numerical experiments and study the behaviour of methods. A comparison of the methods under consideration is given, and the problem of choice of their parameters is discussed.

[1]  V. N. Malozemov,et al.  Finding the Point of a Polyhedron Closest to the Origin , 1974 .

[2]  V. F. Demʹi︠a︡nov,et al.  Introduction to minimax , 1976 .

[3]  H. Kunzi,et al.  Lectu re Notes in Economics and Mathematical Systems , 1975 .

[4]  Philip Wolfe,et al.  Finding the nearest point in A polytope , 1976, Math. Program..

[5]  V. F. Demʹi︠a︡nov,et al.  Introduction to minimax , 1976 .

[6]  R. Mifflin Semismooth and Semiconvex Functions in Constrained Optimization , 1977 .

[7]  A. A. Goldstein,et al.  Optimization of lipschitz continuous functions , 1977, Math. Program..

[8]  Jorge J. Moré,et al.  Recent Developments in Algorithms and Software for Trust Region Methods , 1982, ISMP.

[9]  B. Korte,et al.  Mathematical Programming the State of the Art: Bonn 1982 , 1983 .

[10]  F. Clarke Optimization And Nonsmooth Analysis , 1983 .

[11]  Antony R. Unwin,et al.  Progress in Nondifferentiable Optimisation , 1983 .

[12]  D. Mayne,et al.  On the Extension of Constrained Optimization Algorithms from Differentiable to Nondifferentiable Problems , 1983 .

[13]  John E. Dennis,et al.  Numerical methods for unconstrained optimization and nonlinear equations , 1983, Prentice Hall series in computational mathematics.

[14]  K. Kiwiel Methods of Descent for Nondifferentiable Optimization , 1985 .

[15]  V. F. Dem'yanov,et al.  Nondifferentiable Optimization , 1985 .

[16]  On the Steepest-Descent Method for a Class of Quasi-Differentiable Optimization Problems , 1985 .

[17]  Diethard Pallaschke,et al.  Nondifferentiable Optimization: Motivations and Applications , 1985 .

[18]  D. Mayne,et al.  Algorithm Models for Nondifferentiable Optimization , 1985 .

[19]  L. Polyakova On minimizing the sum of a convex function and a concave function , 1986 .

[20]  Vladimir F. Demyanov,et al.  Nonsmoothness and quasidifferentiability , 1986 .

[21]  K. Kiwiel A linearization method for minimizing certain quasidifferentiable functions , 1986 .

[22]  V. Demyanov,et al.  An algorithm for minimizing a certain class of quasidifferentiable functions , 1986 .

[23]  Continuous Generalized Gradients for Nonsmooth Functions , 1988 .

[24]  Liqun Qi,et al.  Quasidifferentials and maximal normal operators , 1990, Math. Program..

[25]  Adil M. Bagirov,et al.  A method of approximating a quasidifferential , 1992 .

[26]  C. Lemaréchal,et al.  A Condensed Introduction to Bundle Methods in Nonsmooth Optimization , 1994 .

[27]  Emilio Spedicato,et al.  Algorithms for Continuous Optimization , 1994 .

[28]  Boris N. Pshenichnyj The Linearization Method for Constrained Optimization , 1994 .

[29]  V. F. Demʹi︠a︡nov,et al.  Constructive nonsmooth analysis , 1995 .

[30]  P. Panagiotopoulos,et al.  Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics , 1996 .

[31]  Krzysztof C. Kiwiel,et al.  Restricted Step and Levenberg-Marquardt Techniques in Proximal Bundle Methods for Nonconvex Nondifferentiable Optimization , 1996, SIAM J. Optim..

[32]  Adil M. Bagirov,et al.  A method for minimizing convex functions based on continuous approximations to the subdifferential , 1998 .

[33]  Reformulation of a Problem of Economic Equilibrium , 1998 .

[34]  Adil M. Bagirov Minimization Methods for One Class of Nonsmooth Functions and Calculation of Semi-Equilibrium Prices , 1999 .