Journal ArticleDOI
On solving quadratically constrained quadratic programming problem with one non-convex constraint
TLDR
This problem is transformed to a parametric quadratic programming problem without any non-convex constraint and then by solving the parametric problem via an iterative scheme and updating the parameter in each iteration, the solution of the problem is achieved.Abstract:
In this paper we consider a quadratically constrained quadratic programming problem with convex objective function and many constraints in which only one of them is non-convex. This problem is transformed to a parametric quadratic programming problem without any non-convex constraint and then by solving the parametric problem via an iterative scheme and updating the parameter in each iteration, the solution of the problem is achieved. The convergence of the proposed method is investigated. Numerical examples are given to show the applicability of the new method.read more
Citations
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Journal ArticleDOI
On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints
TL;DR: In this paper , the authors studied the minimization of an indefinite quadratic function over the intersection of balls and linear inequality constraints (QOBL) and showed that the optimal solution of QOBL can be found by solving several extended trust region subproblems (e-TRS).
Journal ArticleDOI
A hybrid method for solving non-convex min–max quadratic fractional problems under quadratic constraints
TL;DR: In this article, a non-convex min-max fractional problem of quadratic functions subject to convex and non-consistency constraints is studied, using the Dinkelbach-type method.
References
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Book
Computers and Intractability: A Guide to the Theory of NP-Completeness
TL;DR: The second edition of a quarterly column as discussed by the authors provides a continuing update to the list of problems (NP-complete and harder) presented by M. R. Garey and myself in our book "Computers and Intractability: A Guide to the Theory of NP-Completeness,” W. H. Freeman & Co., San Francisco, 1979.
Book
Convex Optimization
Stephen Boyd,Lieven Vandenberghe +1 more
TL;DR: In this article, the focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them, and a comprehensive introduction to the subject is given. But the focus of this book is not on the optimization problem itself, but on the problem of finding the appropriate technique to solve it.
Journal ArticleDOI
Benchmarking optimization software with performance profiles
Elizabeth D. Dolan,Jorge J. Moré +1 more
TL;DR: It is shown that performance profiles combine the best features of other tools for performance evaluation to create a single tool for benchmarking and comparing optimization software.
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