Conventional Lagrangean preprocessing for the network Weight Constrained Shortest Path Problem (WCSPP calculates lower bounds on the cost of using each node and edge in a feasible path using a single optimal Lagrange multiplier for the relaxation of the WCSPP. These lower bounds are used in conjunction with an upper bound to eliminate nodes and … Read more
We consider methods for regularising the least-squares solution of the linear system Ax = b. In particular, we propose iterative methods for solving large problems in which a trust-region bound ||x||
We study approximations of chance constrained problems. In particular, we consider the Sample Average Approximation (SAA) approach and discuss convergence properties of the resulting problem. A method for constructing bounds for the optimal value of the considered problem is discussed and we suggest how one should tune the underlying parameters to obtain a good approximation … Read more
We consider a regression problem where uncertainty affects to the dependent variable of the elements of the database. A model based on the standard epsilon-Support Vector Regression approach is given, where two hyperplanes need to be constructed to predict the interval-valued dependent variable. By using the Hausdorff distance to measure the error between predicted and … Read more
In this work, we consider a classification problem where the objects to be classified are bags of instances which are vectors measuring d different attributes. The classification rule is defined in terms of a ball, whose center and radius are the parameters to be computed. Given a bag, it is assigned to the positive class … Read more
Systems of polynomial equations over an algebraically-closed field K can be used to concisely model many combinatorial problems. In this way, a combinatorial problem is feasible (e.g., a graph is 3-colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution over K. In this paper, we investigate an algorithm … Read more
The problem of Routing and Wavelength Assignment in Wavelength Division Multiplexing (WDM) optical networks consists in routing a set of lightpaths and assigning a wavelength to each of them, such that lightpaths whose routes share a common fiber are assigned to different wavelengths. When the objective is to minimize the total number of wavelengths used, … Read more
Given a graph G = (V,E), the independent set problem is that of finding a maximum-cardinality subset S of V such that no two vertices in S are adjacent. We introduce two fast local search routines for this problem. The first can determine in linear time whether a maximal solution can be improved by replacing … Read more
In this paper, oligopolistic competition in a centralized power market is characterized by a multi-leader single-follower game, and formulated as a nonlinear programming (NLP) problem. An AC network is used to represent the transmission system and is modeled using rectangular coordinates. The follower is composed of a set of competitive suppliers, demands, and the system … Read more
An affine supply function equilibrium (SFE) approach is used to discuss voltage constraints and reactive power issues in the modeling of strategic behavior. Generation companies (GenCos) can choose their bid parameters with no restrictions for both energy and spinning reserves. The strategic behavior of generators is formulated as a multi-leader single-follower game. Each GenCo is … Read more