6 papers
Algebraic Farkas Lemma and Strong Duality for Perturbed Conic Linear Programming
P. D. Khanh, V. V. H. Khoa, T. H. Mo
This paper addresses the study of algebraic versions of Farkas lemma and strong duality results in the very broad setting of infinite-dimensional conic linear programming in dual p…
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…
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…
General Derivative-Free Optimization Methods under Global and Local Lipschitz Continuity of Gradients
Pham Duy Khanh, Boris S. Mordukhovich, Dat Ba Tran
This paper addresses the study of derivative-free smooth optimization problems, where the gradient information on the objective function is unavailable. Two novel general derivativ…
On Second-order Conditions for Quasiconvexity and Pseudoconvexity of -smooth Functions
Pham Duy Khanh, Vo Thanh Phat
For a -smooth function on a finite-dimensional space, a necessary condition for its quasiconvexity is the positive semidefiniteness of its Hessian matrix on the subs…
Variational Inequalities Governed By Strongly Pseudomonotone Operators
Pham Tien Kha, Pham Duy Khanh
Qualitative and quantitative aspects for variational inequalities governed by strongly pseudomonotone operators on Hilbert space are investigated in this paper. First, we establish…