Bilevel Programming and the Separation Problem

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MILPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MILPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is … Read more

Risk-Averse Control of Undiscounted Transient Markov Models

We use Markov risk measures to formulate a risk-averse version of the undiscounted total cost problem for a transient controlled Markov process. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed. We illustrate the results on an optimal stopping … Read more

Learning how to play Nash, potential games and alternating minimization method for structured nonconvex problems on Riemannian manifolds

In this paper we consider minimization problems with constraints. We show that if the set of constaints is a Riemannian manifold of non positive curvature and the objective function is lower semicontinuous and satisfi es the Kurdyka-Lojasiewicz property, then the alternating proximal algorithm in Euclidean space is naturally extended to solve that class of problems. We … Read more

A Refined Gomory-Chvátal Closure for Polytopes in the Unit Cube

We introduce a natural strengthening of Gomory-Chvátal cutting planes for the important class of 0/1-integer programming problems and study the properties of the elementary closure that arises from the new class of cuts. Most notably, we prove that the new closure is polyhedral, we characterize the family of all facet-defining inequalities, and we compare it … Read more

New updates of incomplete LU factorizations and applications to large nonlinear systems

In this paper, we address the problem of preconditioning sequences of large sparse nonsymmetric systems of linear equations and present two new strategies to construct approximate updates of factorized preconditioners. Both updates are based on the availability of an incomplete LU (ILU) factorization for one matrix of the sequence and differ in the approximation of … Read more

On Differentiability Properties of Player Convex Generalized Nash Equilibrium Problems

This article studies differentiability properties for a reformulation of a player convex generalized Nash equilibrium problem as a constrained and possibly nonsmooth minimization problem. By using several results from parametric optimization we show that, apart from exceptional cases, all locally minimal points of the reformulation are differentiability points of the objective function. This justifies a … Read more

Limited Memory Block Krylov Subspace Optimization for Computing Dominant Singular Value Decompositions

In many data-intensive applications, the use of principal component analysis (PCA) and other related techniques is ubiquitous for dimension reduction, data mining or other transformational purposes. Such transformations often require efficiently, reliably and accurately computing dominant singular value decompositions (SVDs) of large unstructured matrices. In this paper, we propose and study a subspace optimization technique … Read more

Scatter search algorithms for the single row facility layout problem

The single row facility layout problem (SRFLP) is the problem of arranging facilities with given lengths on a line, with the objective of minimizing the weighted sum of the distances between all pairs of facilities. The problem is NP-hard and research has focused on heuristics to solve large instances of the problem. In this paper … Read more

Economic and Environmental Analysis of Photovoltaic Energy Systems via Robust Optimization

This paper deals with the problem of determining the optimal size of a residential grid-connected photovoltaic system to meet a certain CO2 reduction target at a minimum cost. Ren et al. proposed a novel approach using a simple linear programming that minimizes the total energy costs for residential buildings in Japan. However, their approach is … Read more

Approximate Maximum Principle for Discrete Approximations of Optimal Control Systems with Nonsmooth Objectives and Endpoint Constraints

The paper studies discrete/finite-difference approximations of optimal control problems governed by continuous-time dynamical systems with endpoint constraints. Finite-difference systems, considered as parametric control problems with the decreasing step of discretization, occupy an intermediate position between continuous-time and discrete-time (with fixed steps) control processes and play a significant role in both qualitative and numerical aspects of … Read more