Solving the canonical dual of box- and integer-constrained nonconvex quadratic programs via a deterministic direct search algorithm

DOI10.1080/10556788.2011.641125zbMath1270.90041OpenAlexW1972604104MaRDI QIDQ4924117

David Yang Gao, David R. Easterling, William I. Thacker, Stephen C. Billups, Layne T. Watson

Publication date: 30 May 2013

Published in: Optimization Methods and Software (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10556788.2011.641125

zbMATH Keywords

global optimizationinteger programmingcanonical duality theoryalgorithm VTDIRECT

Mathematics Subject Classification ID

Integer programming (90C10) Nonconvex programming, global optimization (90C26) Quadratic programming (90C20) Optimality conditions and duality in mathematical programming (90C46)

Related Items (4)

Global solutions to nonconvex optimization of 4th-order polynomial and log-sum-exp functions ⋮ Canonical Dual Approach for Minimizing a Nonconvex Quadratic Function over a Sphere ⋮ On quadratically constrained quadratic optimization problems and canonical duality theory ⋮ Canonical dual approach to solving the maximum cut problem

Uses Software

• VTDIRECT95

Cites Work

• Global extremal conditions for multi-integer quadratic programming
• Solutions and optimality criteria for nonconvex constrained global optimization problems with connections between canonical and Lagrangian duality
• Checking local optimality in constrained quadratic programming is NP- hard
• Lipschitzian optimization without the Lipschitz constant
• Computational experience with a new class of convex underestimators: Box-constrained NLP problems
• A branch-and-cut algorithm for nonconvex quadratic programs with box constraints
• Dynamic data structures for a direct search algorithm
• A reformulation-convexification approach for solving nonconvex quadratic programming problems
• Duality principles in nonconvex systems. Theory, methods and applications
• Solutions and optimality criteria to box constrained nonconvex minimization problems
• A new class of improved convex underestimators for twice continuously differentiable constrained NLPs
• Algorithm 897
• Some NP-complete problems in quadratic and nonlinear programming
• Deterministic global optimization in nonlinear optimal control problems
• Canonical dual transformation method and generalized triality theory in nonsmooth global optimization

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