Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
Theory of duality in mathematical programming
Theory of duality in mathematical programming
Quadratic programming is in NP
Information Processing Letters
Nonlinear optimization: complexity issues
Nonlinear optimization: complexity issues
On affine scaling algorithms for nonconvex quadratic programming
Mathematical Programming: Series A and B
Global optimality criterion and a duality with a zero gap in nonconvex optimization
SIAM Journal on Mathematical Analysis
Diewert-Crouzeix conjugation for general quasiconvex duality and applications
Journal of Optimization Theory and Applications
Dual approach to minimization on the set of Pareto-optimal solutions
Journal of Optimization Theory and Applications
Convex analysis and variational problems
Convex analysis and variational problems
Nonlinear Analysis: Theory, Methods & Applications
Journal of Global Optimization
Augmented Lagrangian Duality and Nondifferentiable Optimization Methods in Nonconvex Programming
Journal of Global Optimization
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Introduction to Global Optimization (Nonconvex Optimization and Its Applications)
Complete Solutions and Extremality Criteria to Polynomial Optimization Problems
Journal of Global Optimization
The bounds of feasible space on constrained nonconvex quadratic programming
Journal of Computational and Applied Mathematics
A study on concave optimization via canonical dual function
Journal of Computational and Applied Mathematics
A review of recent advances in global optimization
Journal of Global Optimization
Global optimization by canonical dual function
Journal of Computational and Applied Mathematics
Solution to an optimal control problem via canonical dual method
Journal of Control Science and Engineering
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
Global optimization over a box via canonical dual function
Journal of Computational and Applied Mathematics
Counterexamples to some triality and tri-duality results
Journal of Global Optimization
SIAM Journal on Optimization
Duality and solutions for quadratic programming over single non-homogeneous quadratic constraint
Journal of Global Optimization
Applying the canonical dual theory in optimal control problems
Journal of Global Optimization
Global minimizer of large scale stochastic rosenbrock function: canonical duality approach
ICONIP'12 Proceedings of the 19th international conference on Neural Information Processing - Volume Part IV
Solution to singular optimal control by backward differential flow
Journal of Control Science and Engineering
Journal of Global Optimization
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This paper presents a perfect duality theory and a complete set of solutions to nonconvex quadratic programming problems subjected to inequality constraints. By use of the canonical dual transformation developed recently, a canonical dual problem is formulated, which is perfectly dual to the primal problem in the sense that they have the same set of KKT points. It is proved that the KKT points depend on the index of the Hessian matrix of the total cost function. The global and local extrema of the nonconvex quadratic function can be identified by the triality theory [11]. Results show that if the global extrema of the nonconvex quadratic function are located on the boundary of the primal feasible space, the dual solutions should be interior points of the dual feasible set, which can be solved by deterministic methods. Certain nonconvex quadratic programming problems in {\open {R}}^{n} can be converted into a dual problem with only one variable. It turns out that a complete set of solutions for quadratic programming over a sphere is obtained as a by-product. Several examples are illustrated.