Triangulation of a three-dimensional point from $n\ge 2$ two-dimensional images can be formulated as a quadratically constrained quadratic program. We propose an algorithm to extract candidate solutions to this problem from its semidefinite programming relaxations. We then describe a sufficient condition and a polynomial time test for certifying when such a solution is optimal. This … Read more
Operations Research (OR) is the discipline of applying advanced analytical methods to help make better decisions (Horner (2003)). OR is characterized by its broad applicability and its interdisciplinary nature. Currently, in addition to mathematics, many other undergraduate programs such as management sciences, business, economics, electrical engineering, civil engineering, chemical engineering, and related fields, have incorporated … Read more
In this paper, we address the optimal energy storage management and sizing problem in the presence of renewable energy and dynamic pricing. We formulate the problem as a stochastic dynamic programming problem that aims to minimize the long-term average cost of conventional generation used as well as investment in storage, if any, while satisfying all … Read more
Purpose: To describe and mathematically validate the superiorization methodology, which is a recently-developed heuristic approach to optimization, and to discuss its applicability to medical physics problem formulations that specify the desired solution (of physically given or otherwise obtained constraints) by an optimization criterion. Methods: The superiorization methodology is presented as a heuristic solver for a … Read more
In this paper is presented the problem of optimizing a functional over a Pareto control set associated with a convex multiobjective control problem in Hilbert spaces, namely parabolic system. This approach generalizes for this setting some results obtained in finite dimensions. Some examples are presented. General optimality results are obtained, and a special attention is … Read more
In this paper, we consider a first-order block-decomposition method for minimizing the sum of a convex differentiable function with Lipschitz continuous gradient, and two other proper closed convex (possibly, nonsmooth) functions with easily computable resolvents. The method presented contains two important ingredients from a computational point of view, namely: an adaptive choice of stepsize for … Read more
We provide a family of polytopes P in [0, 1]^n whose Gomory-Chvátal rank is at least ((1 + 1/6)n – 4). Citation Rutcor 640 Bartholomew Road Piscataway, NJ 08854-8003 , July,2012 Article Download View A family of polytopes in the 0/1-cube with Gomory-Chvátal rank at least ((1+1/6)n – 4)
Around a solution of an optimization problem, an “identifiable” subset of the feasible region is one containing all nearby solutions after small perturbations to the problem. A quest for only the most essential ingredients of sensitivity analysis leads us to consider identifiable sets that are “minimal”. This new notion lays a broad and intuitive variational-analytic … Read more
In this short and self contained paper we are proposing a simple penalty, which is a modification on the constraint set. We show that duality gap is eliminated under certain conditions. Citation May,2010 Article Download View Eliminating Duality Gap by Sigma Penalty
A wide range of problems can be modeled as Mixed Integer Linear Programming (MIP) problems using standard formulation techniques. However, in some cases the resulting MIP can be either too weak or too large to be effectively solved by state of the art solvers. In this survey we review advanced MIP formulation techniques that result … Read more