Journal ArticleDOI
Reduction constraints for the global optimization of NLPs
Reads0
Chats0
TLDR
Convergence of branch-and-bound algorithms for the solution of NLPs is obtained by finding ever-nearer lower and upper bounds to the objective function.About:
This article is published in International Transactions in Operational Research.The article was published on 2004-01-01. It has received 23 citations till now. The article focuses on the topics: Feasible region & Linear programming relaxation.read more
Citations
More filters
Journal ArticleDOI
GloMIQO: Global mixed-integer quadratic optimizer
TL;DR: GloMIQO is introduced, a numerical solver addressing mixed-integer quadratically-constrained quadratic programs to $${\varepsilon}$$-global optimality, and its algorithmic components are presented for reformulating user input, detecting special structure including convexity and edge-concavity, generating tight convex relaxations, and finding good feasible solutions.
Journal ArticleDOI
Convex quadratic relaxations for mixed-integer nonlinear programs in power systems
TL;DR: A set of new convex quadratic relaxations for nonlinear and mixed-integer nonlinear programs arising in power systems, providing an interesting alternative to state-of-the-art semidefinite programming relaxations.
Journal ArticleDOI
Global minimization using an Augmented Lagrangian method with variable lower-level constraints
TL;DR: A novel global optimization method based on an Augmented Lagrangian framework is introduced for continuous constrained nonlinear optimization problems and global convergence to an $$varepsilon}$$ -global minimizer of the original problem is proved.
Journal ArticleDOI
Strengthening the SDP Relaxation of AC Power Flows With Convex Envelopes, Bound Tightening, and Valid Inequalities
TL;DR: In this paper, the authors revisited the semidefine programming (SDP) relaxation of the ac power flow equations in light of recent results illustrating the benefits of bounds propagation, valid inequalities, and the convex quadratic relaxation.
Book ChapterDOI
Reformulations in Mathematical Programming: A Computational Approach
TL;DR: A survey of existing reformulations interpreted along these lines, some example applications, and the implementation of a software framework for reformulation and optimization are presented.
References
More filters
Journal ArticleDOI
Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
TL;DR: For nonlinear programming problems which are factorable, a computable procedure for obtaining tight underestimating convex programs is presented to exclude from consideration regions where the global minimizer cannot exist.
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.
Journal ArticleDOI
A global optimization method, αBB, for general twice-differentiable constrained NLPs — I. Theoretical advances
TL;DR: The deterministic global optimization algorithm, αBB (α-based Branch and Bound) is presented, which offers mathematical guarantees for convergence to a point arbitrarily close to the global minimum for the large class of twice-differentiable NLPs.
Journal ArticleDOI
Global optimization of nonconvex NLPs and MINLPs with applications in process design
TL;DR: Computational results demonstrate that the algorithm compares very favorably to several other current approaches when applied to a large collection of global optimization and process design problems, typically faster, requires less storage and it produces more accurate results.
Journal ArticleDOI
A new reformulation-linearization technique for bilinear programming problems
TL;DR: This paper is concerned with the development of an algorithm for general bilinear programming problems, and develops a new Reformulation-Linearization Technique (RLT) for this problem, and imbeds it within a provably convergent branch-and-bound algorithm.