Convex analysis and variational problems
Convex analysis and variational problems
Nonlinear Analysis: Theory, Methods & Applications
Journal of Global Optimization
Canonical Duality Theory and Solutions to Constrained Nonconvex Quadratic Programming
Journal of Global Optimization
Complete Solutions and Extremality Criteria to Polynomial Optimization Problems
Journal of Global Optimization
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Non-convex quadratic minimization problems with quadratic constraints: global optimality conditions
Mathematical Programming: Series A and B
Global optimization for a class of fractional programming problems
Journal of Global Optimization
Solutions to quadratic minimization problems with box and integer constraints
Journal of Global Optimization
Canonical dual least square method for solving general nonlinear systems of quadratic equations
Computational Optimization and Applications
Solutions to quadratic minimization problems with box and integer constraints
Journal of Global Optimization
Canonical dual least square method for solving general nonlinear systems of quadratic equations
Computational Optimization and Applications
Counterexamples to some triality and tri-duality results
Journal of Global Optimization
Duality Gap Estimation of Linear Equality Constrained Binary Quadratic Programming
Mathematics of Operations Research
Second-order Kuhn-Tucker invex constrained problems
Journal of Global Optimization
On zero duality gap in nonconvex quadratic programming problems
Journal of Global Optimization
On duality gap in binary quadratic programming
Journal of Global Optimization
On reduction of duality gap in quadratic knapsack problems
Journal of Global Optimization
Canonical duality theory and algorithm for solving challenging problems in network optimisation
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part III
Computational Optimization and Applications
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This paper presents a canonical duality theory for solving a general nonconvex quadratic minimization problem with nonconvex constraints. By using the canonical dual transformation developed by the first author, the nonconvex primal problem can be converted into a canonical dual problem with zero duality gap. A general analytical solution form is obtained. Both global and local extrema of the nonconvex problem can be identified by the triality theory associated with the canonical duality theory. Illustrative applications to quadratic minimization with multiple quadratic constraints, box/integer constraints, and general nonconvex polynomial constraints are discussed, along with insightful connections to classical Lagrangian duality. Criteria for the existence and uniqueness of optimal solutions are presented. Several numerical examples are provided.