It is well known that the eigenvalues of a real symmetric matrix are not everywhere differentiable. A classical result of Ky Fan states that each eigenvalue of a symmetric matrix is the difference of two convex functions. This directly implies that the eigenvalues of a symmetric matrix are semismooth everywhere. Based on a very recent … Read more
We define a class of parabolic problems with control and state constraints and identify a problem within this class which possesses a locally unique critical point satisfying the second order sufficient optimality conditions. In this solution inequality constraints on the control are strongly active. The second derivative of the Lagrangian is not globally coercive. This … Read more
We consider the solution of Mixed Integer Nonlinear Programming (MINLP) problems by a parallel implementation of nonlinear branch-and-bound on a computational grid or meta-computer. Computational experience on a set of large MINLPs is reported which indicates that this approach is efficient for the solution of large MINLPs. Citation Numerical Analysis Report NA/200, Department of Mathematics, … Read more
We propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP+PR) for the Steiner problem in graphs. In this multi-start approach, the greedy randomized construction phase of a GRASP is replaced by the use of several construction heuristics with a weight perturbation strategy that combines intensification and diversification elements, as in … Read more
The floorplanning (or facility layout) problem consists in finding the optimal positions for a given set of modules of fixed area (but perhaps varying dimensions) within a facility such that the distances between pairs of modules that have a positive connection cost are minimized. This is a hard discrete optimization problem; even the restricted version … Read more
Long-term hydrothermal coordination is one of the main problems to be solved by an electric utility. Its solution provides the optimal allocation of hydraulic, thermal and nuclear resources at the different intervals of the planning horizon. The purpose of the paper is twofold. Firstly, it presents a new package for solving the hydrothermal coordination problem. … Read more
In chemical engineering complex dynamic optimization problems formulated on moving horizons have to be solved on-line. In this work, we present a multiscale approach based on wavelets where a hierarchy of successively, adaptively refined problems are constructed.They are solved in the framework of nested iteration as long as the real-time restrictions are fulfilled. To avoid … Read more
In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization … Read more
Weighted sum based approaches to multiobjective optimization is computationally very efficient. However,they have two main weakness: 1) Only one Pareto solution can be obtained in one run 2) The solutions in the concave part of the Pareto front cannot be obtained. This paper proposes a new theory on multiobjective optimization using weighted aggregation approach. Based … Read more
We investigate the solution of large scale instances of the capacitated and uncapacitated facility location problems. Let n be the number of customers and m the number of potential facility sites. For the uncapacitated case we solved instances of size m x n=3000 x 3000; for the capacitated case the largest instances were 1000 x … Read more