Journal ArticleDOI
A Simplicial Branch-and-Bound Method for Solving Nonconvex All-Quadratic Programs
TLDR
The presented algorithm often outperforms a comparable rectangular branch-and-bound method and under the assumption that a feasible point of the all-quadratic program is known, the algorithm guarantees an ε-approximate optimal solution in a finite number of iterations.Abstract:
In this paper we present an algorithm for solving nonconvex quadratically constrained quadratic programs (all-quadratic programs). The method is based on a simplicial branch-and-bound scheme involving mainly linear programming subproblems. Under the assumption that a feasible point of the all-quadratic program is known, the algorithm guarantees an e-approximate optimal solution in a finite number of iterations. Computational experiments with an implementation of the procedure are reported on randomly generated test problems. The presented algorithm often outperforms a comparable rectangular branch-and-bound method.read more
Citations
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Journal ArticleDOI
A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs
TL;DR: In this article, a branch-and-bound algorithm for solving nonconvex quadratically-constrained quadratic programs is proposed, where branching is done by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles.
Journal ArticleDOI
Packing equal circles in a square: a deterministic global optimization approach
Marco Locatelli,Ulrich Raber +1 more
TL;DR: The optimality within a given tolerance of best known solutions in the literature for n= 10-35, n = 38, 39 will be proved, with the exception of the case n= 32 for which a new solution has been detected and proved to be optimal within the given tolerance.
Posted Content
General Heuristics for Nonconvex Quadratically Constrained Quadratic Programming
Jaehyun Park,Stephen Boyd +1 more
TL;DR: The Suggest-and-Improve framework for general nonconvex quadratically constrained quadratic programs (QCQPs) is introduced and an open-source Python package QCQP is introduced, which implements the heuristics discussed in the paper.
Journal ArticleDOI
Global optimization approach to unequal sphere packing problems in 3D
TL;DR: A variety of algorithms are proposed which improve markedly the existing simplicial branch-and-bound algorithm for the general nonconvex quadratic program and heuristic algorithms are incorporated to strengthen the efficiency of the algorithm.
Journal ArticleDOI
A Bi-Level Branch and Bound Method for Economic Dispatch With Disjoint Prohibited Zones Considering Network Losses
TL;DR: In this paper, a bi-level branch-and-bound (B&B) method was proposed to solve the economic dispatch problem with prohibited zones and network losses, which can be transformed into a mixed-integer quadratically constrained quadratic programming (MIQCQP), where linear relaxation technique is applied on each bilinear term.
References
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Book
Sphere packings, lattices, and groups
TL;DR: The second edition of this book continues to pursue the question: what is the most efficient way to pack a large number of equal spheres in n-dimensional Euclidean space?
Book
Global Optimization: Deterministic Approaches
Reiner Horst,Tuy Hoang +1 more
TL;DR: This study develops a unifying approach to constrained global optimization that provides insight into the underlying concepts and properties of diverse techniques recently proposed to solve a wide variety of problems encountered in the decision sciences, engineering, operations research and other disciplines.
BookDOI
Handbook of global optimization
TL;DR: This paper presents algorithms for global optimization of mixed-integer nonlinear programs using the Reformulation-Linearization/Convexification Technique (RLT) and an introduction to dynamical search.
Journal ArticleDOI
Jointly Constrained Biconvex Programming
Faiz A. Al-Khayyal,James E. Falk +1 more
TL;DR: It is proved that the minimum of a biconcave function over a nonempty compact set occurs at a boundary point of the set and not necessarily an extreme point and the algorithm is proven to converge to a global solution of the nonconvex program.