In this paper we continue the development of a theoretical foundation for efficient primal-dual interior-point algorithms for convex programming problems expressed in conic form, when the cone and its associated barrier are self-scaled (see [NT97]). The class of problems under consideration includes linear programming, semidefinite programming and convex quadratically constrained quadratic prog...

A function f is said to be cone superadditive if there exists a partition of R into a family of polyhedral convex cones such that f(z + x) + f(z + y) ≤ f(z) + f(z + x+ y) holds whenever x and y belong to the same cone in the family. This concept is useful in nonlinear integer programming in that, if the objective function is cone superadditive, the global minimality can be characterized by loca...

The main purpose of these lectures is to familiarize the student with the basic ingredients of convex analysis, especially its subdifferential calculus. This is done while moving to a clearly discernible end-goal, the Karush-Kuhn-Tucker theorem, which is one of the main results of nonlinear programming. Of course, in the present lectures we have to limit ourselves most of the time to the Karush...

This paper is about a computer application for planning maintenance of aircraft fleet in what regards allocation skilled technicians. The formalization this mathematical programming problem written as minimizing one. decision variables are the data number available technicians, working hours needed to accomplish maintenance, costs due daily operation facilities, and downtime. Although, non-line...

We propose a framework for building preconditioners for sequences of linear systems of the form (A+∆k)xk = bk, where A is symmetric positive semidefinite and ∆k is diagonal positive semidefinite. Such sequences arise in several optimization methods, e.g., in affine-scaling methods for bound-constrained convex quadratic programming and bound-constrained linear least squares, as well as in trust-...

Abstract In this paper we present general-purpose preconditioners for regularized augmented systems, and their corresponding normal equations, arising from optimization problems. We discuss positive definite preconditioners, suitable CG MINRES. consider “sparsifications" which avoid situations in eigenvalues of the preconditioned matrix may become complex. Special attention is given to systems ...