Hidden conic quadratic representation of some nonconvex quadratic optimization problems

• Published in: Mathematical programming Vol. 143; no. 1-2; pp. 1 - 29
• Main Authors: Ben-Tal, Aharon, den Hertog, Dick
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2014; Springer Nature B.V
• Subjects: Analysis; Calculus of Variations and Optimal Control; Optimization; Combinatorics; Conics; Full Length Paper; Inequality; Linear programming; Mathematical and Computational Physics; Mathematical Methods in Physics; Mathematics; Mathematics and Statistics; Mathematics of Computing; Numerical Analysis; Optimization; Quadratic programming; Studies; Theoretical; 90C20; Robust optimization; Conic Quadratic Program; Hidden convexity; Implementation error; 90C26; Simultaneous diagonalizability; S-lemma

The problem of minimizing a quadratic objective function subject to one or two quadratic constraints is known to have a hidden convexity property, even when the quadratic forms are indefinite. The equivalent convex problem is a semidefinite one, and the equivalence is based on the celebrated S-lemma...