Linear programming: active set analysis and computer programs
Linear programming: active set analysis and computer programs
Some NP-complete problems in quadratic and nonlinear programming
Mathematical Programming: Series A and B
A collection of test problems for constrained global optimization algorithms
A collection of test problems for constrained global optimization algorithms
On the continuity of the minimum in parametric quadratic programs
Journal of Optimization Theory and Applications
On Standard Quadratic Optimization Problems
Journal of Global Optimization
A Decomposition Method for Global and Local Quadratic Minimization
Journal of Global Optimization
Decomposition Methods for Solving Nonconvex Quadratic Programs via Branch and Bound*
Journal of Global Optimization
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We present a method which when applied to certain non-convex QP will locatethe globalminimum, all isolated local minima and some of the non-isolated localminima. The method proceeds by formulating a (multi) parametric convex QP interms ofthe data of the given non-convex QP. Based on the solution of the parametricQP,an unconstrained minimization problem is formulated. This problem ispiece-wisequadratic. A key result is that the isolated local minimizers (including theglobalminimizer) of the original non-convex problem are in one-to-one correspondencewiththose of the derived unconstrained problem.The theory is illustrated with several numerical examples. A numericalprocedure isdeveloped for a special class of non-convex QP‘s. It is applied to a problemfrom theliterature and verifies a known global optimum and in addition, locates apreviously unknown local minimum.