We give a detailed numerical and theoretical analysis of a stabilization problem posed by V. Blondel in 1994. Our approach illustrates the effectiveness of a new gradient sampling algorithm for finding local optimizers of nonsmooth, nonconvex optimization problems arising in control, as well as the power of nonsmooth analysis for understanding variational problems involving polynomial … Read more
We present a review of several professional software products that serve to analyze and solve nonlinear (global and local) optimization problems across a variety of hardware and software environments. The product versions discussed have been implemented for compiler platforms, spreadsheets, algebraic (optimization) modeling languages, and for integrated scientific-technical computing systems. The discussion highlights some of … Read more
When dealing with extremely hard global optimization problems, i.e. problems with a large number of variables and a huge number of local optima, heuristic procedures are the only possible choice. In this situation, lacking any possibility of guaranteeing global optimality for most problem instances, it is quite difficult to establish rules for discriminating among different … Read more
In this paper a special step control problem is considered. The formulation of the problem uses a parameter to control the switching point. By using Taylor’s increment methods first and second order optimality conditions (in the sense of Pontryagin’s maximum principle) will be derived. Citation Preprint 2005-1, Department of Mathematics and Computer Science, Technical University … Read more
Inverse approaches and, in particular, intensity modulated radiotherapy (IMRT), in combination with the development of new technologies such as multi-leaf collimators (MLCs), have enabled new potentialities of radiotherapy for cancer treatment. The main mathematical tool needed in this connection is numerical optimization. In this article, the variety of continuous optimization approaches, which have been proposed … Read more
In this paper we present an interior point method for large scale Signorini elastic contact problems. We study the case of an elastic body in frictionless contact with a rigid foundation. Primal and primal-dual algorithms are developed to solve the quadratic optimization problem arising in the variational formulation. Our computational study confirms the efficiency of … Read more
We present an original method for partitioning by automatic classi- fication, using the optimization technique of tabu search. The method uses a classical tabu search scheme based on transfers for the minimization of the within variance; it introduces in the tabu list the indicator of the object transfered. This method is compared with two stochastic … Read more
Using a moment interpretation of recent results on sum-of-squares decompositions of non-negative polynomial matrices, we propose a hierarchy of convex linear matrix inequality (LMI) relaxations to solve non-convex polynomial matrix inequality (PMI) optimization problems, including bilinear matrix inequality (BMI) problems. This hierarchy of LMI relaxations generates a monotone sequence of lower bounds that converges to … Read more
This paper presents a new data classification method based on mixed-integer programming. Traditional approaches that are based on partitioning the data sets into two groups perform poorly for multi-class data classification problems. The proposed approach is based on the use of hyper-boxes for defining boundaries of the classes that include all or some of the … Read more
We consider a networked system defined on a graph where each edge corresponds to a quasilinear hyperbolic system with space dimension one. At the nodes, the system is governed by algebraic node conditions. The system is controlled at the nodes of the graph. Optimal control problems for systems of this type arise in the operation … Read more