box-constrained quadratic programming

Spectral-gauge cuts for semidefinite programming

Published: 2026/07/02

Other Topics box-constrained quadratic programming, cutting-plane algorithm, semidefinite programming, sparse principal component analysis

We use symmetric gauge theory to develop a general class of cutting-plane algorithms for semidefinite programming. We formulate a separation problem based on spectral normalizations induced by gauges and derive a closed-form separation oracle. This oracle yields an implementable cut-generation procedure that, by varying the gauge, recovers standard cut families and generates new ones with … Read more

Extended Triangle Inequalities for Nonconvex Box-Constrained Quadratic Programming

Published: 2025/01/12

Bound-constrained Optimization, Global Optimization Theory, Quadratic Programming box-constrained quadratic programming, nonconvex quadratic programming, triangle inequalities

Let Box_n = {x in R^n : 0<= x <= e }, and let QPB_n denote the convex hull of {(1, x’)'(1, x’) : x in Box_n}. The quadratic programming problem min{x’Q x + q’x : x in Box_n} where Q is not positive semidefinite (PSD), is equivalent to a linear optimization problem over QPB_n … Read more