RESEARCH
with Boris Mordukhovich, Mau Nam Nguyen and Tuyen Tran
The paper presents a new approach to solve multifacility location problems, which is based on mixed integer programming and algorithms for minimizing differences of convex (DC) functions. The main challenges for solving the multifacility location problems under consideration come from their intrinsic discrete, nonconvex, and nondifferentiable nature. We provide a reformulation of these problems as those of continuous optimization and then develop a new DC type algorithm for their solutions involving Nesterov's smoothing. The proposed algorithm is computationally implemented via MATLAB numerical tests on both artificial and real data sets.
with Warren Hare and Yves Lucet
Computing explicitly the {\epsilon}-subdifferential of a proper function amounts to computing the level set of a convex function namely the conjugate minus a linear function. The resulting theoretical algorithm is applied to the the class of (convex univariate) piecewise linear-quadratic functions for which existing numerical libraries allow practical computations. We visualize the results in a primal, dual, and subdifferential views through several numerical examples. We also provide a visualization of the Brøndsted-Rockafellar Theorem.
Work-in-Progress:
DC Programming Algorithm for Fully Convex Bilevel Optimization
with Boris Mordukhovich, Alain Zemkoho, and Vuong Phan
Solving a Continuous Max-Min Problem by DC Algorithms
with Boris Mordukhovich, Mau Nam Nguyen and Tuyen Tran
Solving Linear Complimentarity Problem involving hidden-Z matrices
with S.K.Neogy, Gambheer Singh and Sajal Ghosh