The Intentional Controlled Islanding (ICI) and the Black Start Allocation (BSA) are two examples of problems in the power systems literature that have been formulated as Mixed Integer Programs (MIPs). A key consideration in both of these problems is that each island must have at least one energized generator. In this paper, we provide three … Read more
We present strong mixed-integer programming (MIP) formulations for high-dimensional piecewise linear functions that correspond to trained neural networks. These formulations can be used for a number of important tasks, such as verifying that an image classification network is robust to adversarial inputs, or solving decision problems where the objective function is a machine learning model. … Read more
High school timetabling problems consist in building periodic timetables for class-teacher meetings considering compulsory and non-compulsory requisites. This family of problems has been widely studied since the 1950s, mostly via mixed-integer programming and metaheuristic techniques. However, the efficient obtention of optimal or near-optimal solutions is still a challenge for many problems of practical size. In … Read more
In this note, some results are introduced considering the assumptions of quasiconvexity and nonmonotonicity, finally an application and an idea to solve the quasiconvex equilibrium problem are presented considering these new results. ArticleDownload View PDF
We provide sharp worst-case evaluation complexity bounds for nonconvex minimization problems with general inexpensive constraints, i.e.\ problems where the cost of evaluating/enforcing of the (possibly nonconvex or even disconnected) constraints, if any, is negligible compared to that of evaluating the objective function. These bounds unify, extend or improve all known upper and lower complexity bounds … Read more
Given two arbitrary closed sets in Euclidean space, a simple transversality condition guarantees that the method of alternating projections converges locally, at linear rate, to a point in the intersection. Exact projection onto nonconvex sets is typically intractable, but we show that computationally-cheap inexact projections may suffice instead. In particular, if one set is defined … Read more
We propose a new data-driven approach for addressing multi-stage stochastic linear optimization problems with unknown distributions. The approach consists of solving a robust optimization problem that is constructed from sample paths of the underlying stochastic process. We provide asymptotic bounds on the gap between the optimal costs of the robust optimization problem and the underlying … Read more
We consider optimization problems over the Stiefel manifold whose objective function is the summation of a smooth function and a nonsmooth function. Existing methods for solving this kind of problems can be classified into three classes. Algorithms in the first class rely on information of the subgradients of the objective function and thus tend to … Read more
The separable convex resource allocation problem with nested bound constraints aims to allocate $B$ units of resources to $n$ activities to minimize a separable convex cost function, with lower and upper bounds on the total amount of resources that can be consumed by nested subsets of activities. We develop a new combinatorial algorithm to solve … Read more
Many real-world decision-making problems can be modeled as network design problems, especially on networks with capacity requirements on links. In network design problems, decisions are made on installation of flow transfer capacities on the links and routing of flow from a set of source nodes to a set of sink nodes through the links. Many … Read more