Showing papers by "Aharon Ben-Tal published in 1980"
TL;DR: In this article, the Hessians of a local minimum of a mathematical programming problem with equality and inequality constraints are derived. But the main object is to derive second-order conditions, involving the Hessian of the functions, or related results where some other curvature information is used.
Abstract: This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.
157 citations
01 Jan 1980
TL;DR: Two important solution concepts in the theory of multicriteria decision making are Pareto optimum and Lexicographic optimum.
Abstract: Two important solution concepts in the theory of multicriteria decision making are Pareto optimum and Lexicographic optimum.
87 citations
01 Jan 1980
TL;DR: In this paper, the Dubovitskii-Milyutin theory of local optimality for optimization problems in topological vector spaces was introduced, and the essentials of a unified second-order theory of necessary conditions were introduced, within which it is possible to obtain second order conditions for problems in Calculus of Variation, Optimal Control, Mathematical Programming and Semi-infinite Programming.
Abstract: The paper introduces the essentials of a unified second-order theory of local optimality (necessary conditions) for optimization problems in topological vector spaces. The results contain the first order conditions, as expressed in the Dubovitskii-Milyutin Theory, and form a framework within which it is possible to obtain second order conditions for problems in Calculus of Variation, Optimal Control, Mathematical Programming and Semi-infinite Programming.
32 citations
TL;DR: In this paper, the authors give characterization of optimal solutions for convex semi-infinite programming problems, and overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn-Tucker theories.
Abstract: This paper gives characterization of optimal Solutions for convex semiinfinite programming problems. These characterizations are free of a constraint qualification assumption. Thus they overcome the deficiencies of the semiinfinite versions of the Fritz John and the Kuhn-Tucker theories, which give only necessary or sufficient conditions for optimality, but not both.
17 citations
TL;DR: The rate of convergence of line search algorithms based on general interpolating functions is derived and is shown to be independent of the particular interpolating function used and this result holds for the root finding problem $f(x) = 0$ as well.
Abstract: The rate of convergence of line search algorithms based on general interpolating functions is derived and is shown to be independent of the particular interpolating function used. This result holds for the root finding problem $f(x) = 0$ as well. We show how inverse interpolation can be used in conjunction with the line search problem and derive its rate of convergence. Our analysis suggests that one-point line search algorithms (in particular Newton's method) are inefficient in a sense. Two-point algorithms using rational interpolating functions are recommended.
12 citations