Displaying similar documents to “A stability theorem in nonlinear bilevel programming.”

A second order η -approximation method for constrained optimization problems involving second order invex functions

Tadeusz Antczak (2009)

Applications of Mathematics

Similarity:

A new approach for obtaining the second order sufficient conditions for nonlinear mathematical programming problems which makes use of second order derivative is presented. In the so-called second order η -approximation method, an optimization problem associated with the original nonlinear programming problem is constructed that involves a second order η -approximation of both the objective function and the constraint function constituting the original problem. The equivalence between...

Regions of stability for ill-posed convex programs

Sanjo Zlobec (1982)

Aplikace matematiky

Similarity:

Regions of stability are chunks of the space of parameters in which the optimal solution and the optimal value depend continuously on the data. In these regions the problem of solving an arbitrary convex program is a continuous process and Tihonov's regularization is possible. This paper introduces a new region we furnisch formulas for the marginal value. The importance of the regions of stability is demostrated on multicriteria decision making problems and in calculating the minimal...

LFS functions in multi-objective programming

Luka Neralić, Sanjo Zlobec (1996)

Applications of Mathematics

Similarity:

We find conditions, in multi-objective convex programming with nonsmooth functions, when the sets of efficient (Pareto) and properly efficient solutions coincide. This occurs, in particular, when all functions have locally flat surfaces (LFS). In the absence of the LFS property the two sets are generally different and the characterizations of efficient solutions assume an asymptotic form for problems with three or more variables. The results are applied to a problem in highway construction,...

Saddle points criteria via a second order η -approximation approach for nonlinear mathematical programming involving second order invex functions

Tadeusz Antczak (2011)

Kybernetika

Similarity:

In this paper, by using the second order η -approximation method introduced by Antczak [3], new saddle point results are obtained for a nonlinear mathematical programming problem involving second order invex functions with respect to the same function η . Moreover, a second order η -saddle point and a second order η -Lagrange function are defined for the so-called second order η -approximated optimization problem constructed in this method. Then, the equivalence between an optimal solution...