General lagrange-type functions in constrained global optimization part II: Exact auxiliary functions

This paper is a continuation of [13]. For each constrained optimization problem we consider certain unconstrained problems, which are constructed by means of auxiliary (Lagrange-type) functions. We study only exact auxiliary functions, it means that the set of their global minimizers coincides with the solution set of the primal constrained optimization problem. Sufficient conditions for the exactness of an auxiliary function are given. These conditions are obtained without assumption that the Lagrange function has a saddle point. Some examples of exact auxiliary functions are given.

[1]  Vitali G. Zhadan,et al.  General lagrange-type functions in constrained global optimization Part I: auxiliary functions and optimality conditions , 2001 .

[2]  Diethard Pallaschke,et al.  Foundations of mathematical optimization : convex analysis without linearity , 1997 .

[3]  A. M. RubinovSchool.  Decreasing Functions with Applications to Penalization 1 , 1997 .

[4]  V. Zhadan.  On some estimates of the penalty coefficient in methods of exact penalty functions , 1985 .

[5]  D. M. Ryan,et al.  A New Method for Constrained Optimization Problems , 1969, Oper. Res..

[6]  Vitali G. Zhadan,et al.  Exact Auxiliary Functions in Non-Convex Optimization , 1992 .

[7]  M. Bazaraa,et al.  Sufficient conditions for a globally exact penalty function without convexity , 1982 .

[8]  D. D. Morrison.  Optimization by Least Squares , 1968 .

[9]  L. Grippo,et al.  Exact penalty functions in constrained optimization , 1989 .

[10]  J. Burke.  An exact penalization viewpoint of constrained optimization , 1991 .

[11]  S. Dolecki,et al.  Exact Penalties for Local Minima , 1979 .

[12]  Dimitri P. Bertsekas,et al.  Constrained Optimization and Lagrange Multiplier Methods , 1982 .

[13]  Jon W. Tolle,et al.  Exact penalty functions in nonlinear programming , 1973, Math. Program..

[14]  Yuri G. Evtushenko,et al.  Exact auxiliary functions , 1990 .

[15]  M. Andramonov.  An Approach to Constructing Generalized Penalty Functions , 2001 .

[16]  A. Rubinov.  Abstract Convexity and Global Optimization , 2000 .

[17]  W. Zangwill.  Non-Linear Programming Via Penalty Functions , 1967 .

[18]  X. Q. Yang,et al.  Decreasing Functions with Applications to Penalization , 1999, SIAM J. Optim..

[19]  I. I. Eremin.  The penalty method in convex programming , 1967 .

[20]  C. Charalambous.  A negative-positive barrier method for non-linear programming , 1976 .

[21]  I. Singer.  Abstract Convex Analysis , 1997 .

[22]  V. G. Zhadan,et al.  Exact auxiliary functions in optimization problems , 1991 .

[23]  Francisco Facchinei,et al.  Exact penalization via dini and hadamard conditional derivatives , 1998 .

[24]  Xiaoqi Yang,et al.  Extended Lagrange And Penalty Functions in Continuous Optimization , 1999 .