subspace methods – Optimization Online

A Minimal-Gradient Subspace Method for Unconstrained Optimization

Published: 2026/08/10

We propose a minimal-gradient subspace method for unconstrained optimization. For strictly convex quadratics, conjugate gradient can be interpreted as exact minimization over a two-dimensional affine subspace. We use the same reduced subspace in the nonlinear case, but compute a trial step by minimizing a local model of the next gradient norm. For SPD quadratics, every … Read more

Semidefinite optimization, a spectral approach

Published: 2002/09/30

M.A. van Bossum

Nonlinear Optimization, Semi-definite Programming convex optimization, eigenvalue optimization, iterative methods, large-scale optimization, newton methods, semidefinite programming, spectral method, subspace methods

This thesis is about mathematical optimization. Mathematical optimization involves the construction of methods to solve optimization problems, which can arise from real-life problems in applied science, when they are mathematically modeled. Examples come from electrical design, engineering, control theory, telecommunication, environment, finance, and logistics. This thesis deals especially with semidefinite optimization problems. Semidefinite programming is … Read more