This paper proposes an algorithm to efficiently solve large optimization problems which exhibit a column bounded block-diagonal structure, where subproblems differ in right-hand side and cost coefficients. Similar problems are often tackled using cutting-plane algorithms, which allow for an iterative and decomposed solution of the problem. When solving subproblems is computationally expensive and the set … Read more
Polynomial interpolation or regression models are an important tool in Derivative-free Optimization, acting as surrogates of the real function. In this work, we propose the use of these models in the multiobjective framework of directional direct search, namely the one of Direct Multisearch. Previously evaluated points are used to build quadratic polynomial models, which are … Read more
We analyze worst-case complexity of a Proximal augmented Lagrangian (Proximal AL) framework for nonconvex optimization with nonlinear equality constraints. When an approximate first-order (second-order) optimal point is obtained in the subproblem, an $\epsilon$ first-order (second-order) optimal point for the original problem can be guaranteed within $\mathcal{O}(1/ \epsilon^{2 – \eta})$ outer iterations (where $\eta$ is a … Read more
Random projections map a set of points in a high dimensional space to a lower dimen- sional one while approximately preserving all pairwise Euclidean distances. While random projections are usually applied to numerical data, we show they can be successfully applied to quadratic programming formulations over a set of linear inequality constraints. Instead of solving … Read more
Standard results in stochastic convex optimization bound the number of samples that an algorithm needs to generate a point with small function value in expectation. In this work, we show that a wide class of such algorithms on strongly convex problems can be augmented with sub-exponential confidence bounds at an overhead cost that is only … Read more
The distributed operating room (OR) scheduling problem aims to find an assignment of surgeries to ORs across collaborating hospitals that share their waiting lists and ORs. We propose a stochastic extension of this problem where surgery durations are considered to be uncertain. In order to obtain solutions for the challenging stochastic model, we use sample … Read more
In this paper we study the auxiliary problems that appear in p-order tensor methods for unconstrained minimization of convex functions with \nu-Holder continuous pth derivatives. This type of auxiliary problems corresponds to the minimization of a (p+\nu)-order regularization of the pth order Taylor approximation of the objective. For the case p=3, we consider the use … Read more
Two-stage stochastic programming is a mathematical framework widely used in real- life applications such as power system operation planning, supply chains, logistics, inventory management, and financial planning. Since most of these problems cannot be solved analytically, decision makers make use of numerical methods to obtain a near-optimal solution. Some applica- tions rely on the implementation … Read more
The inventory routing problem (IRP) is an integrated inventory and transportation planning problem that jointly determines the replenishment schedules for a given set of retailers, and the routing decisions for a supplier that distributes a product to the retailers over a finite planning horizon typically consisting of multiple periods. In the classical IRP, retailers are … Read more
The Distance Geometry Problem (DGP) seeks to find positions for a set of points in geometric space when some distances between pairs of these points are known. The so-called discretization assumptions allow to discretize the search space of DGP instances. In this paper, we focus on a key subclass of DGP, namely the Discretizable Molecular … Read more