7 papers · 1 filter
Applications of Variational Analysis to a Generalized Heron Problem
Boris Mordukhovich, Nguyen Mau Nam, Juan Salinas
This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized dif…
Constraint Qualifications and Optimality Conditions for Nonconvex Semi-Infinite and Infinite Programs
B. S. Mordukhovich, T. T. A. Nghia
The paper concerns the study of new classes of nonlinear and nonconvex optimization problems of the so-called infinite programming that are generally defined on infinite-dimensiona…
Rated Extremal Principles for Finite and Infinite Systems
Boris S. Mordukhovich, Hung M. Phan
In this paper we introduce new notions of local extremality for finite and infinite systems of closed sets and establish the corresponding extremal principles for them called here…
Quantitative Stability of Linear Infinite Inequality Systems under Block Perturbations with Applications to Convex Systems
M. J. Cánovas, M. A. LóPez, B. S. Mordukhovich +1
The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over…
Tangential Extremal Principles for Finite and Infinite Systems of Sets, I: Basic Theory
Boris S. Mordukhovich, Hung M. Phan
In this paper we develop new extremal principles in variational analysis that deal with finite and infinite systems of convex and nonconvex sets. The results obtained, unified unde…
Tangential Extremal Principles for Finite and Infinite Systems of Sets, II: Applications to Semi-infinite and Multiobjective Optimization
Boris S. Mordukhovich, Hung M. Phan
This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and…