MATHEMATICAL ENGINEERING TECHNICAL REPORTS Using Multiparameter Eigenvalues for Solving Quadratic Programming with Quadratic Equality Constraints
نویسندگان
چکیده
We show that multiparameter eigenvalues can solve some optimization problems. Specifically, we develop an eigenvalue-based algorithm for quadratic programming with quadratic equality constraints (QECQP). QECQP models various well-known optimization problems such as the maximum-cut problem, and QECQP is also closely related to quadratically constrained quadratic programming (QCQP). Recently, for some special cases of QCQP with one or two constraints, algorithms based on eigenvalue with one or two parameter have been proposed, which can solve some nonconvex instances, for which ordinary optimization methods often fail. In this paper, we generalize the aforementioned eigenvalue-based algorithms by allowing for larger number of constraints; using multiparameter eigenvalue problems, we propose an algorithm that is applicable to QECQP with an arbitrary fixed number of constraints. Unfortunately, the algorithm is not proved to find a global solution. However, we show in experiments that our algorithm works for small-scale instances and computes a global solution with high accuracy, as long as the effects of singular matrices are small enough for our algorithm to work well.
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تاریخ انتشار 2016