The Uncapacitated Single Allocation p-Hub Median Problem with Stepwise Cost Function

In this paper, we address a new version of the Uncapacitated Single Allocation p-Hub Median Problem (USApHMP) in which transportation costs on each edge are given by piecewise constant cost functions. In the classical USApHMP, transportation costs are modelled as linear functions of the transport volume, where a fixed discount factor on hub-hub connections is … Read more

Semidefinite approximations of the polynomial abscissa

Given a univariate polynomial, its abscissa is the maximum real part of its roots. The abscissa arises naturally when controlling linear differential equations. As a function of the polynomial coefficients, the abscissa is H\”older continuous, and not locally Lipschitz in general, which is a source of numerical difficulties for designing and optimizing control laws. In … Read more

A survey on operator splitting and decomposition of convex programs

Many structured convex minimization problems can be modeled by the search of a zero of the sum of two monotone operators. Operator splitting methods have been designed to decompose and regularize at the same time these kind of models. We review here these models and the classical splitting methods. We focus on the numerical sensitivity … Read more

Asymptotic Behaviour of the Quadratic Knapsack Problem

We study subclasses of the quadratic knapsack problem, where the profits are independent random variables defined on the interval [0,1] and the knapsack capacity is proportional to the number of items (we assume that the weights are arbitrary numbers from the interval [0,1]). We show asymptotically that the objective value of a very easy heuristic … Read more

Spectral projected gradient method for stochastic optimization

We consider the Spectral Projected Gradient method for solving constrained optimization problems with the objective function in the form of mathematical expectation. It is assumed that the feasible set is convex, closed and easy to project on. The objective function is approximated by a sequence of Sample Average Approximation functions with different sample sizes. The … Read more


In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this … Read more

Closing the gap in pivot methods for linear programming

We propose pivot methods that solve linear programs by trying to close the duality gap from both ends. The first method maintains a set $\B$ of at most three bases, each of a different type, in each iteration: a primal feasible basis $B^p$, a dual feasible basis $B^d$ and a primal-and-dual infeasible basis $B^i$. From … Read more

The Sparse PCA Problem: Optimality Conditions and Algorithms

Sparse principal component analysis (PCA) addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to interpret the principal components, and is applicable in a wide variety of fields including genetics and … Read more

A directional distance based super-efficiency DEA model handling negative data

This paper develops a new radial super-efficiency data envelopment analysis (DEA) model, which allows input-output variables to take both negative and positive values. Compared with existing DEA models capable of dealing with negative data, the proposed model can rank the efficient DMUs and is feasible no matter whether the input-output data are non-negative or not. … Read more

Cutting Box Strategy: an algorithmic framework for improving metaheuristics for continuous global optimization

In this work, we present a new framework to increase effectiveness of metaheuristics in seeking good solutions for the general nonlinear optimization problem, called Cutting Box Strategy (CBS). CBS is based on progressive reduction of the search space through the use of intelligent multi-starts, where solutions already obtained cannot be revisited by the adopted metaheuristic. … Read more