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

Tadeusz Antczak (2009)

Applications of Mathematics

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 the nonlinear...

About a special class of nonconvex optimization problems

Libuše Grygarová (1990)

Aplikace matematiky

The article deals with certain nonconvex optimization problem which have features analogous to those of the linear optimization problems. We can find their absolute extrema and the set all optimal points of such nonconvex optimization problem represents the closure of a face of a spherical polyhedron which is its feasible set.

About the Problem of Disjunctive Programming

Ivan I. Eremin (2000)

The Yugoslav Journal of Operations Research

An approach to robust network design in telecommunications

Georgios Petrou, Claude Lemaréchal, Adam Ouorou (2007)

RAIRO - Operations Research

In telecommunications network design, one of the most frequent problems is to adjust the capacity on the links of the network in order to satisfy a set of requirements. In the past, these requirements were demands based on historical data and/or demographic predictions. Nowadays, because of new technology development and customer movement due to competitiveness, the demands present considerable variability. Thus, network robustness w.r.t demand uncertainty is now regarded as a major consideration....

An SQP method for mathematical programs with complementarity constraints with strong convergence properties

Matus Benko, Helmut Gfrerer (2016)

Kybernetika

We propose an SQP algorithm for mathematical programs with complementarity constraints which solves at each iteration a quadratic program with linear complementarity constraints. We demonstrate how strongly M-stationary solutions of this quadratic program can be obtained by an active set method without using enumeration techniques. We show that all limit points of the sequence of iterates generated by our SQP method are at least M-stationary.

Applications of the Fréchet subdifferential

Durea, M. (2003)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 46A30, 54C60, 90C26.In this paper we prove two results of nonsmooth analysis involving the Fréchet subdifferential. One of these results provides a necessary optimality condition for an optimization problem which arise naturally from a class of wide studied problems. In the second result we establish a sufficient condition for the metric regularity of a set-valued map without continuity assumptions.