We propose a stabilized model for the electricity generation management problem on a yearly scale. We also introduce an original and efficient solution method in a particular case. Our model is compared to other management methods and offers the best average cost while preserving a reasonable standard deviation of the cost over a set of … Read more
Nonconvex quadratic programming (QP) is an NP-hard problem that optimizes a general quadratic function over linear constraints. This paper introduces a new global optimization algorithm for this problem, which combines two ideas from the literature—finite branching based on the first-order KKT conditions and polyhedral-semidefinite relaxations of completely positive (or copositive) programs. Through a series of … Read more
We introduce an inexact Gauss-Newton trust-region method for solving bound-constrained nonlinear least-squares problems where, at each iteration, a trust-region subproblem is approximately solved by the Conjugate Gradient method. Provided a suitable control on the accuracy to which we attempt to solve the subproblems, we prove that the method has global and asymptotic fast convergence properties. … Read more
The adaptive cubic regularization method [Cartis, Gould, Toint, 2009-2010] has been recently proposed for solving unconstrained minimization problems. At each iteration of this method, the objective function is replaced by a cubic approximation which comprises an adaptive regularization parameter whose role is related to the local Lipschitz constant of the objective’s Hessian. We present new … Read more
Admission control problems have been studied extensively in the past. In a typical setting, resources like bandwidth have to be distributed to the different customers according to their demands maximizing the profit of the company. Yet, in real-world applications those demands are deviating and in order to satisfy their service requirements often a robust approach … Read more
In this paper, we investigate the recoverable robust knapsack problem, where the uncertainty of the item weights follows the approach of Bertsimas and Sim (2003,2004). In contrast to the robust approach, a limited recovery action is allowed, i.e., upto k items may be removed when the actual weights are known. This problem is motivated by … Read more
We introduce an adaptive algorithm to estimate the uncertain parameter of a stochastic optimization problem. The procedure estimates the one-step-ahead means, variances and covariances of a random process in a distribution-free and multidimensional framework when these means, variances and covariances are slowly varying on a given past interval. The quality of the approximate problem obtained … Read more
We consider robust formulations of the mid-term optimal power management problem. For this type of problems, classical approaches minimize the expected generation cost over a horizon of one year, and model the uncertain future by means of scenario trees. In this setting, extreme scenarios -with low probability in the scenario tree- may fail to be … Read more
We consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic center of a polytope. We show that the problem has a dual of the same form and give complexity results for several different … Read more
We recommend an implementation of the Markowitz problem to generate stable portfolios with respect to perturbations of the problem parameters. The stability is obtained proposing novel calibrations of the covariance matrix between the returns that can be cast as convex or quasiconvex optimization problems. A statistical study as well as a sensitivity analysis of the … Read more