A new quasi-Newton scheme for updating a low rank positive semi-definite Hessian approximation is described, primarily for use in sequential quadratic programming methods for nonlinear programming. Where possible the symmetric rank one update formula is used, but when this is not possible a new rank two update is used, which is not in the Broyden family, although invariance under linear transfo...

In this short paper, we recall the use of squared slacks used to transform inequality constraints into equalities and several reasons why their introduction may be harmful in many algorithmic frameworks routinely used in nonlinear programming. Numerical examples performed with the sequential quadratic programming method illustrate those reasons. Our results are reproducible with state-of-the-ar...

We consider the problem of approximating the global minimum of a general quadratic program (QP) with n variables subject to m ellipsoidal constraints. For m = 1, we rigorously show that an-minimizer, where error 2 (0; 1), can be obtained in polynomial time, meaning that the number of arithmetic operations is a polynomial in n, m, and log(1==). For m 2, we present a polynomial-time (1 ? 1 m 2)-a...

In this work we present an algorithm for the solution of multiparametric linear and quadratic programming problems.With linear constraints and linear or convex quadratic objective functions, the optimal solution of these optimization problems is given by a conditional piecewise linear function of the varying parameters. This function results from first-order estimations of the analytical nonlin...

We show that possibilistic quadratic programs with crisp decision variables and continuous fuzzy number coefficients are well-posed, i.e. small changes in the membership function of the coefficients may cause only a small deviation in the possibility distribution of the objective function.

The primal-dual algorithm of parametric linear programming (e.g. {l]) can be extended in some sence to parametric quadratic programming problems as follows. § 1. Problem of the first type Let us consider the following quadratic programming problem PIA with a parameter A. where C is an n X n positive semi-definite matrix, A is an m X n matrix, p and x are n-vectors, and band d are m-vectors. We ...

A fItrite element scheme (together with a conjugate gradient algorithmj is demonstrated to be a very effective method for analyzing general elastoplastic torsion of prismatic bars posed as quadratic programming problems. Solutions for bars with elliptical and Sokolovsky’s oval cross-sections are presented. The solutions for the elliptical bars agree with the existing elastic and limit plastic s...

We are considering the application of the Augmented Lagrangian algorithms with quadratic penalty, to convex problems of quadratic programming. The problems of quadratic programming are composites of quadratic objective function and linear constraints. This important class of problems will be generated through the algorithm of sequential quadratic programming, where at each iteration the quadrat...

The paper covers a formulation of the inverse quadratic programming problem in terms of unconstrained optimization where it is required to find the unknown parameters (the matrix of the quadratic form and the vector of the quasi-linear part of the quadratic form) provided that approximate estimates of the optimal solution of the direct problem and those of the target function to be minimized in...