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Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations

Ruth Misener, Christodoulos A. Floudas
2012 Mathematical programming  
quadratic programs (MIQCQP) to ε-global optimality.  ...  We propose a deterministic global optimization approach, whose novel contributions are rooted in the edge-concave and piecewise-linear underestimators, to address nonconvex mixed-integer quadratically-constrained  ...  We also thank the COIN-OR GAMSLinks Developer Stefan Vigerske for suggesting routines in the GAMSLinks code base that helped us link our MIQCQP solver to GAMS.  ... 
doi:10.1007/s10107-012-0555-6 fatcat:kw2orckkkfax7kjqoug3r72wue

Global optimization of nonconvex problems with multilinear intermediates

Xiaowei Bao, Aida Khajavirad, Nikolaos V. Sahinidis, Mohit Tawarmalani
2014 Mathematical Programming Computation  
We embed this cutting plane generation strategy at every node of the branch-and-reduce global solver BARON, and carry out an extensive computational study on quadratically constrained quadratic problems  ...  We consider global optimization of nonconvex problems containing multilinear functions.  ...  [2] consider the generation of multiterm polyhedral relaxations for nonconvex QCQPs.  ... 
doi:10.1007/s12532-014-0073-z fatcat:xni6phwtgjdszhjdbf72ox7fge

Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming

Tiago Andrade, Fabricio Oliveira, Silvio Hamacher, Andrew Eberhard
2018 Journal of Global Optimization  
These relaxations constitute a key component for some methods for solving nonconvex mixed-integer quadratically constrained quadratic programming (MIQCQP) problems.  ...  We propose methods for improving the relaxations obtained by the normalized multiparametric disaggregation technique (NMDT).  ...  It is a general method with important subclasses including (nonconvex) quadratic programming (QP), mixed-integer programming (MIP), (nonconvex) quadratically constrained quadratic programming (QCQP), and  ... 
doi:10.1007/s10898-018-0728-9 fatcat:cnfjx65dundw7iuurvre7agnva

Global optimization advances in Mixed-Integer Nonlinear Programming, MINLP, and Constrained Derivative-Free Optimization, CDFO

Fani Boukouvala, Ruth Misener, Christodoulos A. Floudas
2016 European Journal of Operational Research  
This manuscript reviews recent advances in deterministic global optimization for Mixed-Integer Nonlinear Programming (MINLP), as well as Constrained Derivative-Free Optimization (CDFO).  ...  Finally, an inclusive and complete test suite is provided for both MINLP and CDFO algorithms, which is useful for future benchmarking.  ...  MIQCQP, MIQCP, QAP, Box-Constrained MIQP A mixed-integer quadratically-constrained quadratic program (MIQCQP) is defined as a MINLP where all of the nonlinearities are quadratic; symbols have the same  ... 
doi:10.1016/j.ejor.2015.12.018 fatcat:jwe7b7ivrzhrjbttdl74eff2pe

Dynamically generated cutting planes for mixed-integer quadratically constrained quadratic programs and their incorporation into GloMIQO 2

Ruth Misener, James B. Smadbeck, Christodoulos A. Floudas
2014 Optimization Methods and Software  
The Global Mixed-Integer Quadratic Optimizer, GloMIQO, addresses mixed-integer quadratically-constrained quadratic programs (MIQCQP) to ε-global optimality.  ...  Novel contributions of this paper include: development of a corollary to Crama's [35] necessary and sufficient condition for the existence of a cut dominating the termwise relaxation of a bilinear expression  ...  Global optimisation of quadratically-constrained quadratic programs (QCQP) using dynamically-generated supporting hyperplanes was first introduced by Audet et al. [14] .  ... 
doi:10.1080/10556788.2014.916287 fatcat:3nzggkbdovevfprdirytdjruz4

Domain reduction techniques for global NLP and MINLP optimization

Yash Puranik, Nikolaos V. Sahinidis
2017 Constraints  
Domain reduction techniques are especially important in speeding up convergence to the global optimum for challenging nonconvex nonlinear programming (NLP) and mixed-integer nonlinear programming (MINLP  ...  In this work, we survey the various techniques used for domain reduction of NLP and MINLP optimization problems.  ...  Annals of Operations Research 149, 37-41 (2007) Multiterm polyhedral relaxations for non- convex, quadratically-constrained quadratic programs.  ... 
doi:10.1007/s10601-016-9267-5 fatcat:drn6m456x5dhteazf4uem33bki

14th International Symposium on Mathematical Programming

1990 Mathematical programming  
It is shown that for the success of the variant dom must ful ll a regularity property and that the choice of the normal vectors must meet some demands.Both requirements are ful lled if dom is polyhedral  ...  A v ariation of bundle methods is presented by means of which such a t ype of problems can be solved.In this variation a dynamic polyhedral model of dom is generated by means of normal vectors.In addition  ...  We present a n i n terior-point method for solving quadratically constrained convex quadratic programs.  ... 
doi:10.1007/bf01580875 fatcat:3jtclwmntzgjxkqs5uecombdaa

An Adaptive Refinement Algorithm for Discretizations of Nonconvex QCQP

Akshay Gupte, Arie M. C. A. Koster, Sascha Kuhnke, Christian Schulz, Bora Uçar
We present an iterative algorithm to compute feasible solutions in reasonable running time to quadratically constrained quadratic programs (QCQPs), which form a challenging class of nonconvex continuous  ...  quadratic programs with complementarity constraints and disjoint bilinear programs, demonstrates the effectiveness of our approach.  ...  "Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs". In: Optimization Methods and Software 24.4-5 (2009), pp. 485-504. 31 (b) Zoomed summary.  ... 
doi:10.4230/lipics.sea.2022.24 fatcat:iqwfqw7rsrhhlctytxw7hynwpi

Exploiting structure in nonconvex quadratic optimisation

Radu Baltean-Lugojan, Ruth Misener, Panos Parpas, Engineering And Physical Sciences Research Council, IBM
We explore relevant engineering trade-offs for sparsity patterns on quadratic programming with box constraints, showing they may immediately extend to quadratically constrained instances.  ...  This thesis addresses two arising challenges: specific commercially-relevant pooling problems that bundle bilinear nonconvexities with a topological and polyhedral structure; semidefinite relaxations (  ...  For the discussion in Section 6.2, we consider nonconvex quadratic problems that are box and linearly constrained.  ... 
doi:10.25560/79281 fatcat:ihc7fhtr7bfffivjxe7hqgw62e

Tighter relaxations in mixed-integer nonlinear programming [article]

Benjamin Müller, Technische Universität Berlin, Technische Universität Berlin, Thorsten Koch
For this reason, the contribution of this thesis is to present new methods to construct and strengthen relaxations for mixed-integer nonlinear programs.  ...  The most fundamental ingredient in MINLP solvers is the well-known McCormick relaxation for a product of two variables x and y over a box-constrained domain.  ...  Multiterm polyhedral relaxations for nonconvex, quadratically constrained quadratic programs.  ... 
doi:10.14279/depositonce-9889 fatcat:nuxobkthrjf7vdxpjy645rsvdy

Exploiting structure in non-convex quadratic optimization and gas network planning under uncertainty [article]

Jonas Schweiger, Technische Universität Berlin, Technische Universität Berlin, Thorsten Koch
In this vein, we address applications, where nonconvexity in the model and uncertainty in the data pose principal difficulties. The first part of the thesis deals with non-convex quadratic programs.  ...  Third, we strengthen the state-of-the-art relaxation for the pooling problem, a well-known non-convex quadratic problem, which is, for example, relevant in the petrochemical industry.  ...  "Multiterm Polyhedral Relaxations for Nonconvex, Quadratically Constrained Quadratic Pro- grams." In: Optimization Methods & Software 24 (2009), pages 485-504 (cited on pages 13, 24). [BV04] S.  ... 
doi:10.14279/depositonce-6015 fatcat:qpm2prum5bfklpcgszsfc4hvwq