In this paper, we focus on the convergence analysis for the application of the Peaceman-Rachford splitting method to a convex minimization model whose objective function is the sum of a smooth and nonsmooth convex functions. The sublinear convergence rate in term of the worst-case O(1/t) iteration complexity is established if the gradient of the smooth … Read more
The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt … Read more
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