Solutions to Nonconvex Quadratic Programming over One Non-Homogeneous Quadratic Constraint

• Main Authors: Joe-MeiFeng, 馮若梅
• Other Authors: Ruey-Lin Sheu
• Format: Others
• Language: en_US
• Published: 2010
• Online Access: http://ndltd.ncl.edu.tw/handle/10306571462987979794

碩士 === 國立成功大學 === 數學系應用數學碩博士班 === 98 === In this thesis, we discuss the minimum of a quadratic object function with one nonconvex quadratic constraint. We want to find the primal optimal solution via its corresponding canonical dual solution. We propose the relaxed assumption, simultaneously diagonalization via congruence (SDC), rather than traditional Slater condition. Under this relaxed assumption, we prove that we can still use information from dual problem to find the primal optimal solution. The key point is when the primal solution we found via its corresponding dual solution is not the optimal solution, we can apply ``boundirification technique' to find another solution with no duality gap, and this is also the primal optimal solution. With further analysis, this primal nonconvex problem in fact equals a linearly constrained convex problem, which means a quadratic object function with one quadratic constraint is a nice-structured nonconvex problem. Finally, we have a related review and comparison to Stern and Wolkowicz's result in 1995.