2015 article
Canonical Dual Solutions to Quadratic Optimization over One Quadratic Constraint
Xing, W., Fang, S.-C., Sheu, R.-L., & Zhang, L. (2015, February). ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, Vol. 32.
A quadratic optimization problem with one nonconvex quadratic constraint is studied using the canonical dual approach. Under the dual Slater's condition, we show that the canonical dual has a smooth concave objective function over a convex feasible domain, and this dual has a finite supremum unless the original quadratic optimization problem is infeasible. This supremum, when it exists, always equals to the minimum value of the primal problem. Moreover, a global minimizer of the primal problem can be provided by a dual-to-primal conversion plus a "boundarification" technique. Application to solving a quadratic programming problem over a ball is included and an error bound estimation is provided.