In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring to the number of iterations needed … Read more
Given the demand between each origin-destination pair on a network, the planar hub location problem is to locate the multiple hubs anywhere on the plane and to assign the traffic to them so as to minimize the total travelling cost. The trips between any two points can be nonstop (no hubs used) or started by … Read more
We present a global optimization algorithm, Branch-and-Sandwich, for optimistic bilevel programming problems which satisfy a regularity condition in the inner problem. The functions involved are assumed to be nonconvex and twice continuously differentiable. The proposed approach can be interpreted as the exploration of two solution spaces (corresponding to the inner and the outer problems) using … Read more
We propose improvements to some of the best heuristic algorithms for optimal product pricing problem originally designed by Dobson and Kalish in the late 1980’s and in the early 1990’s. Our improvements are based on a detailed study of a fundamental decoupling structure of the underlying mixed integer programming (MIP) problem and on incorporating more … Read more
In this article, we describe a gas portfolio management problem, which is solved with the SDDP (Stochastic Dual Dynamic Programming) algorithm. We present some improvements of this algorithm and focus on methods of pruning Benders’ cuts, that is to say, methods of picking out the most relevant cuts among those which have been computed. Our … Read more
The \emph{interval bounded generalized trust region subproblem} (GTRS) consists in minimizing a general quadratic objective, $q_0(x) \rightarrow \min$, subject to an upper and lower bounded general quadratic constraint, $\ell \leq q_1(x) \leq u$. This means that there are no definiteness assumptions on either quadratic function. We first study characterizations of optimality for this \emph{implicitly} convex … Read more
We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes … Read more
Using a geometric argument, we show that under a reasonable continuity condition, the Clarke subdifferential of a semi-algebraic (or more generally stratifiable) directionally Lipschitzian function admits a simple form: the normal cone to the domain and limits of gradients generate the entire Clarke subdifferential. The characterization formula we obtain unifies various apparently disparate results that … Read more
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring question in regularization approaches is the selection of regularization parameters, and its effect on the solution and on the optimal value of the optimization problem. The sensitivity of the value function to the regularization parameter can be linked directly … Read more
In this paper we study distributionally robust optimization (DRO) problems where the ambiguity set of the probability distribution is defined by the Kullback-Leibler (KL) divergence. We consider DRO problems where the ambiguity is in the objective function, which takes a form of an expectation, and show that the resulted minimax DRO problems can be formulated … Read more