10 papers
Inexact DC Algorithms in Hilbert Spaces with Applications to PDE-Constrained Optimization
P. D. Khanh, V. V. H. Khoa, B. S. Mordukhovich +2
In this paper, we design and apply novel inexact adaptive algorithms to deal with minimizing difference-of-convex (DC) functions in Hilbert spaces. We first introduce I-ADCA, an in…
Complete Characterizations of Well-Posedness in Parametric Composite Optimization
Boris S. Mordukhovich, Peipei Tang, Chengjing Wang
This paper characterizes the well-posedness of Karush-Kuhn-Tucker system for perturbed composite optimization. Using the parabolic regularity, we introduce a novel second-order var…
Regularized Multiobjective Optimization with Directionally Lipschitzian Data
G. C. Bento, J. X. Cruz Neto, J. O. Lopes +2
The paper is devoted to the study of regularized versions of multiobjective optimization problems described by directionally Lipschitzian functions. Such regularizations appear in…
New Location Science Models with Applications to UAV-Based Disaster Relief
Sina Kazemdehbashi, Yanchao Liu, Boris S. Mordukhovich
Natural and human-made disasters can cause severe devastation and claim thousands of lives worldwide. Therefore, developing efficient methods for disaster response and management i…
Convergence of First-Order Algorithms with Momentum from the Perspective of an Inexact Gradient Descent Method
Pham Duy Khanh, Boris Mordukhovich, Dat Ba Tran
This paper introduces a novel inexact gradient descent method with momentum (IGDm) considered as a general framework for various first-order methods with momentum. This includes, i…
Optimal Control of Nonconvex Sweeping Processes with Variable Time via Finite-Difference Approximations
Tan H. Cao, Boris S. Mordukhovich, Dao Nguyen +2
The paper is devoted to the study of a new class of optimal control problems for nonsmooth dynamical systems governed by nonconvex discontinuous differential inclusions of the swee…