7 papers
Stability Analysis of Generalized Multi-Source Weber Problems
N. H. Hai, V. S. T. Long, N. M. Nam +1
This paper presents a stability analysis of the generalized multi-source Weber problems under the influence of data perturbation within the framework of the Minkowski function. Fir…
The Existence and Stability of Generalized Multi-Source Weber Problems
V. S. T. Long, N. M. Nam, T. H. Tai +1
This paper studies the generalized multi-source Weber problem with set-valued targets in the framework of minimal time functions. We first establish the existence of global and loc…
On the Strong Quasiconvexity of Norms and Distance Functions
V. S. T. Long, N. M. Nam
This paper studies the strong quasiconvexity of norm and distance functions in finite-dimensional normed spaces. Although the Euclidean norm is known to be strongly quasiconvex on…
Solving Regularized Multifacility Location Problems with Unknown Number of Centers via Difference-of-Convex Optimization
W. Geremew, V. S. T. Long, N. M. Nam +1
In this paper, we develop optimization methods for a new model of multifacility location problems defined by a Minkowski gauge with Laplace-type regularization terms. The model is…
First-Order Characterizations of Strong Quasiconvexity and a Quasimonotonicity Gap
Nguyen Xuan Duy Bao, Nguyen Mau Nam
We study first-order conditions for Gâteaux differentiable strongly quasiconvex functions on open convex subsets of normed spaces. First, we prove that the value-order gradient con…
Qualitative and Generalized Differentiation Properties of Optimal Value Functions with Applications to Duality
V. S. T. Long, B. S. Mordukhovich, N. M. Nam +1
This paper investigates general and generalized differentiation properties of the optimal value function associated with perturbed optimization problems. Fundamental results on nea…
Nash Equilibrium and Minimax Theorems via Variational Tools of Convex Analysis
Nguyen Xuan Duy Bao, Boris Mordukhovich, Nguyen Mau Nam
In this paper, we first provide a simple variational proof of the existence of Nash equilibrium in Hilbert spaces by using optimality conditions in convex minimization and Schauder…