In this paper we formulate the fuzzy bilevel programming problem and describe one possible approach for formulating a crisp optimization problem being attached to it. Due to the nature of fuzzy bilevel programming this is a crisp bilevel programming problem. We compare our approach with one using multicriterial optimization and show, that both approaches are … Read more
A new method for the efficient solution of free material optimization problems is introduced. The method extends the sequential convex programming (SCP) concept to a class of optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions … Read more
We develop a new active-set method for nonlinear programming problems that solves a regularized linear program to predict the active set and then fixes the active constraints to solve an equality-constrained quadratic program for fast convergence. Global convergence is promoted through the use of a filter. We show that the regularization parameter fulfills the same … Read more
Abstract: After developing necessary background theory, the original primal and dual are specified, and the invariant primal and dual LP’s are defined. Pairs of linear mappings are defined which establish an effectively one-to-one correspondences between solutions to the original and invariant problems. The invariant problems are recast as a fixed-point problem and precise solution conditions … Read more
We consider the problem of approximating a $p\times m$ rational transfer function $H(s)$ of high degree by another $p\times m$ rational transfer function $\hat{H}(s)$ of much smaller degree. We derive the gradients of the $H_2$-norm of the approximation error and show how stationary points can be described via tangential interpolation. CitationTechnical report UCL-INMA-2007.034, Department of … Read more
Given a separable strongly self-concordant function f:Rn -> R, we show the associated spectral function F(X)= (foL)(X) is also strongly self-concordant function. In addition, there is a universal constant O such that, if f(x) is separable self-concordant barrier then O^2F(X) is a self-concordant barrier. We estimate that for the universal constant we have O
A convex body K has associated with it a unique circumscribed ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum volume. We first give a unified, modern exposition of the basic theory of these extremal ellipsoids using the semi-infinite programming approach pioneered by Fritz John in his seminal 1948 paper. We … Read more
Elementary symmetric polynomials can be thought of as derivative polynomials of $E_n(x)=\prod_{i=1,\ldots,n} x_i$. Their associated hyperbolicity cones give a natural sequence of relaxations for $\Re^n_+$. We establish a recursive structure for these cones, namely, that the coordinate projections of these cones are themselves hyperbolicity cones associated with elementary symmetric polynomials. As a consequence of this … Read more
In this paper we present the convergence analysis of the inexact infeasible path-following(IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes … Read more
In this paper we present a cutting plane algorithm for the Set Covering problem. Cutting planes are generated by a “general” (i.e. not based on the “template paradigm”) separation algorithm based on the following idea: i) identify a suitably small subproblem defined by a subset of the constraints of the formulation; ii) run an exact … Read more