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7 papers · 2 filters
The Smallest Enclosing Ball Problem and the Smallest Intersecting Ball Problem: Existence and Uniqueness of Solutions
Boris S. Mordukhovich, Nguyen Mau Nam, Cristina Villalobos
In this paper we study the following problems: given a finite number of nonempty closed subsets of a normed space, find a ball with the smallest radius that encloses all of the set…
Acceleration Control in Nonlinear Vibrating Systems based on Damped Least Squares
V. N. Pilipchuk
A discrete time control algorithm using the damped least squares is introduced for acceleration and energy exchange controls in nonlinear vibrating systems. It is shown that the da…
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 and Optimality Conditions in Convex Semi-Infinite and Infinite Programming
M. J. CÁnovas, M. A. LÓpez, B. S. Mordukhovich +1
This paper concerns parameterized convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional Banach (resp. finite-dimensio…
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…