In this paper we consider minimization problems with constraints. We will show that if the set of constraints is a Finslerian manifold of non positive flag curvature, and the objective function is di fferentiable and satisfi es the property Kurdyka-Lojasiewicz, then the proximal point method is naturally extended to solve that class of problems. We will prove … Read more
This paper describes libcgrpp, a GNU-style dynamic shared Python/C library of the continuous greedy randomized adaptive search procedure (C-GRASP) for bound constrained global optimization. C-GRASP is an extension of the GRASP metaheuristic (Feo and Resende, 1989). After a brief introduction to C-GRASP, we show how to download, install, configure, and use the library through an … Read more
In this paper we propose an algorithm for the global optimization of computationally expensive black–box functions. For this class of problems, no information, like e.g. the gradient, can be obtained and function evaluation is highly expensive. In many applications, however, a lower bound on the objective function is known; in this situation we derive a … Read more
We show that any nonconvex quadratically constrained quadratic program(QCQP) can be represented as a generalized copositive program. In fact,we provide two representations. The first is based on the concept of completely positive (CP) matrices over second order cones, while the second is based on CP matrices over the positive semidefinte cone. Our analysis assumes that … Read more
Minimization of unconstrained objective function in the form of mathematical expectation is considered. Sample Average Approximation – SAA method transforms the expectation objective function into a real-valued deterministic function using large sample and thus deals with deterministic function minimization. The main drawback of this approach is its cost. A large sample of the random variable … Read more
This paper presents an outcome-space outer approximation algorithm for solving the problem of minimizing the product of two convex functions over a compact convex set in $\R^n$. The computational experiences are reported. The proposed algorithm is convergent. Article Download View An Outcome Space Algorithm for Minimizing the Product of Two Convex Functions over a Convex … Read more
We formulate minmax flow problems as a DC. optimization problem. We then apply a DC primal-dual algorithm to solve the resulting problem.The obtained computational results show that the proposed algorithm is efficient thanks to particular structures of the minmax flow problems. Citation 1. An L. T. H. and Tao P. D., The DC (Difference of … Read more
Let $A \in \Omega_n$ be doubly-stochastic $n \times n$ matrix. Alexander Schrijver proved in 1998 the following remarkable inequality \begin{equation} \label{le} per(\widetilde{A}) \geq \prod_{1 \leq i,j \leq n} (1- A(i,j)); \widetilde{A}(i,j) =: A(i,j)(1-A(i,j)), 1 \leq i,j \leq n \end{equation} We prove in this paper the following generalization (or just clever reformulation) of (\ref{le}):\\ For all … Read more
The optimal design of electrical machines can be mathematically modeled as a mixed-integer nonlinear optimization problem. We present six variants of such a problem, and we show, through extensive computational experiments, that, even though they are mathematically equivalent, the differences in the formulations may have an impact on the numerical performances of a local optimization … Read more
Copositive optimization is a quickly expanding scientific research domain with wide-spread applications ranging from global nonconvex problems in engineering to NP-hard combinatorial optimization. It falls into the category of conic programming (optimizing a linear functional over a convex cone subject to linear constraints), namely the cone of all completely positive symmetric nxn matrices, and its … Read more