Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Two characterizations of Pareto minima in convex multicriteria optimization

Sanjo Zlobec — 1984

Aplikace matematiky

Two conditions are given each of which is both necessary and sufficient for a point to be a global Pareto minimum. The first one is obtained by studying programs where each criterion appears as a single objective function, while the second one is given in terms of a "restricted Lagrangian". The conditions are compared with the familiar characterizations of properly efficient and weakly efficient points of Karlin and Geoffrion.

Regions of stability for ill-posed convex programs: An addendum

Sanjo Zlobec — 1986

Aplikace matematiky

The marginal value formula in convex optimization holds in a more restrictive region of stability than that recently claimed in the literature. This is due to the fact that there are regions of stability where the Lagrangian multiplier function is discontinuous even for linear models.

Regions of stability for ill-posed convex programs

Sanjo Zlobec — 1982

Aplikace matematiky

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 index set...

New regions of stability in input optimization

Sheng HuangSanjo Zlobec — 1988

Aplikace matematiky

using point-to-set mappings we identify two new regions of stability in input optimization. Then we extend various results from the literature on optimality conditions, continuity of Lagrange multipliers, and the marginal value formula over the new and some old regions of stability.

LFS functions in multi-objective programming

Luka NeralićSanjo Zlobec — 1996

Applications of Mathematics

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, where...

Page 1

Download Results (CSV)