A partial ellipsoidal approximation scheme for nonconvex homogeneous quadratic optimization with quadratic constraints

摘要

Abstract An efficient partial ellipsoid approximation scheme is presented to find a 1⌈m2⌉documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$frac{1}{lceil {frac{m}{2}}rceil }$$end{document}-approximation solution to the nonconvex homogeneous quadratic optimization with m convex quadratic constraints, where ⌈x⌉documentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$lceil x rceil $$end{document} is the smallest integer larger than or equal to x. If there is an additional nonconvex quadratic constraint beyond the m convex constraints, we can use the new scheme to find a 1mdocumentclass[12pt]{minimal} usepackage{amsmath} usepackage{wasysym} usepackage{amsfonts} usepackage{amssymb} usepackage{amsbsy} usepackage{mathrsfs} usepackage{upgreek} setlength{oddsidemargin}{-69pt} begin{document}$$frac{1}{m}$$end{document}-approximation solution.