ANTI-OPTIMIZATION PROBLEMS ARISING IN OPTIMIZATION OF STRUCTURAL STEELWORK

Optimization problems arising in software architecture

Software architecture is the process of planning and designing a large-scale software, and a fundamental industrial discipline within the field of software engineering. The current body of knowledge in software architecture is a mixture of personal experience and precise methods. In this paper we move a step towards the formalization of this discipline by describing some optimization problems t...

On the Solution of Equality Constrained Quadratic Programming Problems Arising in Optimization Equality Constrained Quadratic Programming Problems Arising in Optimization

We consider the application of the conjugate gradient method to the solution of large equality constrained quadratic programs arising in nonlinear optimization. Our approach is based on a reduced linear system and generates iterates in the null space of the constraints. Instead of computing a basis for this null space, we choose to work directly with the matrix of constraint gradients, computin...

Approximating Hessians in unconstrained optimization arising from discretized problems

We consider Hessian approximation schemes for large-scale unconstrained optimization in the context of discretized problems. The considered Hessians typically present a nontrivial sparsity and partial separability structure. This allows iterative quasi-Newton methods to solve them despite of their size. Structured finitedifference methods and updating schemes based on the secant equation are pr...

On Some Quadratic Optimization Problems Arising in Computer Vision

The goal of this paper is to find methods for solving various quadratic optimization problems, mostly arising from computer vision (image segmentation and contour grouping). We consider mainly two problems: Problem 1. Let A be an n× n Hermitian matrix and let b ∈ C be any vector, maximize z∗Az + z∗b+ b∗z subject to z∗z = 1, z ∈ C. Problem 2. If A is a real n× n symmetric matrix and b ∈ R is any...

On combinatorial optimization problems arising in computer system design