5 papers · 1 filter
Lagrange Multipliers and Duality with Applications to Constrained Support Vector Machine
Nguyen Mau Nam, Gary Sandine, Quoc Tran-Dinh
In this paper, we employ the concept of quasi-relative interior to analyze the method of Lagrange multipliers and establish strong Lagrangian duality for nonsmooth convex optimizat…
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…
On Characterizations of -Quasiconvexity
Nguyen Xuan Duy Bao, Nguyen Mau Nam
We revisit classical gradient characterizations of quasiconvexity and provide corrected proofs that close gaps in earlier arguments. For the differentiable case of -quasiconvex…
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…