Catálogo de publicaciones - libros

We introduce one-sided versions of Lagrangians and perturbations. We relate them, using concepts from generalized convexity. In such a way, we are able to present the main features of duality theory in a general framework encompassing numerous special instances. We focus our attention on the set of multipliers. We look for an interpretation of multipliers as generalized derivatives of the performance function associated with a dualizing parameterization of the given problem.

Monotonic optimization is concerned with optimization problems dealing with multivariate monotonic functions and differences of monotonic functions. For the study of this class of problems a general framework (Tuy, 2000a) has been earlier developed where a key role was given to a separation property of solution sets of monotonic inequalities similar to the separation property of convex sets. In the present paper the separation cut is combined with other kinds of cuts, called reduction cuts, to further exploit the monotonic structure. Branch and cuts algorithms based on an exhaustive rectangular partition and a systematic use of cuts have proved to be much more efficient than the original polyblock and copolyblock outer approximation algorithms.

This article presents an overview of the use of Lagrange-duality bounds within a branch and bound scheme for solving nonconvex global optimization problems. Convergence properties and application possibilities of the method are discussed.

The general quadratic programming problem is a typical multiextrernal optimization problem, which can have local optima different from global optima. This chapter presents an overview of actual results on general quadratic programming, focusing on three topics: optimality conditions, duality and solution methods. Optimality conditions and solution methods are discussed in the sense of global optimization.

This paper provides an expository discussion on using the (RLT) technique as a unifying approach for solving nonconvex polynomial, factorable, and certain black-box optimization problems. The principal RLT construct applies a to add valid inequalities including polynomial and semidefinite cuts, and a to derive higher dimensional tight linear programming relaxations. These relaxations are embedded within a suitable branch-and-bound scheme that converges to a global optimum for polynomial or factorable programs, and results in a method that derives approximate, near-optimal solutions for black-box optimization problems. We present the basic underlying theory, and illustrate the application of this theory to solve various problems.

Bilevel programming problems are hierarchical optimization problems where an objective function is minimized over the graph of the solution set mapping of a parametric optimization problem. In this paper, a selective survey for this living research area is given. Focus is on main recent approaches to solve such problems, on optimality conditions as well as on essential features of this problem class.

We will survey some of the recent successful applications of deterministic global optimization methods to financial problems. Problems to be discussed are mean-risk models under nonconvex transaction cost, minimal transaction unit constraints and cardinality constraints. Also, we will discuss several bond portfolio optimization problems, long term portfolio optimization problems and others.

Problems to be discussed are concave/d.c. minimization problems, minimization of a nonconvex fractional function and a sumn of several fractional functions over a polytope, optimization over a nonconvex efficient set and so on.

Readers will find that a number of difficult global optimization problems have been solved in practice and that there is a big room for applications of global optimization methods in finance.

We give a brief overview of a rapidly emerging interdisciplinary research area of optimization techniques in medicine. Applying optimization approaches proved to be successful in various medical applications. We identify the main research directions and describe several important problems arising in this area, including disease diagnosis, risk prediction, treatment planning, etc.

The present review paper summarizes the research work done mostly by the authors on packing equal circles in the unit square in the last years.

Complete extensions of based on are presented hereafter in order to solve which can be formulated as . This involves the consideration of variables of different kinds: real, integer, logical or categorical. In order to solve interesting with an important number of variables, some accelerating procedures must be introduced in these extended algorithms. They are based on and are explained in this chapter. In order to validate the designing methodology, are considered. The corresponding is recalled and some are presented and discussed.