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A review of recent advances in global optimization

C. A. Floudas, C. E. Gounaris
2008 Journal of Global Optimization  
with grey box/nonfactorable models, and bilevel nonlinear optimization.  ...  It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization  ...  Acknowledgements Christodoulos A.  ... 
doi:10.1007/s10898-008-9332-8 fatcat:72fpfq72hrdzhf6mxqyc6ssezm

Page 5314 of Mathematical Reviews Vol. , Issue 84m [page]

1984 Mathematical Reviews  
Branching methods for solving integer linear optimization problems. 3. Practical problems and mathematical modelling 4.  ...  Authors’ summary: “We propose a branch-and-bound algorithm for solving the quadratic assignment problem.  ... 

Branch and Bound Based Coordinate Search Filter Algorithm for Nonsmooth Nonconvex Mixed-Integer Nonlinear Programming Problems [chapter]

Florbela P. Fernandes, M. Fernanda P. Costa, Edite M. G. P. Fernandes
2014 Lecture Notes in Computer Science  
We present a methodology to solve nonsmooth nonconvex MINLP problems based on a branch and bound paradigm and a stochastic strategy.  ...  A mixed-integer nonlinear programming problem (MINLP) is a problem with continuous and integer variables and at least, one nonlinear function.  ...  The authors wish to thank two anonymous referees for their valuable comments and suggestions to improve the paper.  ... 
doi:10.1007/978-3-319-09129-7_11 fatcat:to6tjwu5xre2fo54w5okyyanh4

Mixed-integer nonlinear optimization

Pietro Belotti, Christian Kirches, Sven Leyffer, Jeff Linderoth, James Luedtke, Ashutosh Mahajan
2013 Acta Numerica  
Spatial Branch-and-Bound The best-known method for solving nonconvex MINLP problems is branch-and-bound (BB).  ...  Worse, nonconvex integer optimization problems are in general undecidable (Jeroslow, 1973 ).  ... 
doi:10.1017/s0962492913000032 fatcat:drrzy4alsvflbgs6gospgsgnaa

A Lagrangean based branch-and-cut algorithm for global optimization of nonconvex mixed-integer nonlinear programs with decomposable structures

Ramkumar Karuppiah, Ignacio E. Grossmann
2007 Journal of Global Optimization  
In this work we present a global optimization algorithm for solving a class of large-scale nonconvex optimization models that have a decomposable structure.  ...  We propose a specialized deterministic branch-and-cut algorithm to solve these models to global optimality, wherein bounds on the global optimum are obtained by solving convex relaxations of these models  ...  In particular, we propose a branch-and-cut framework for solving problem (P) to global optimality wherein we solve a convex relaxation of the original nonconvex model with cuts added to it in order to  ... 
doi:10.1007/s10898-007-9203-8 fatcat:sexy6vipzndmxcrwa2fo6sqq7m

A review and comparison of solvers for convex MINLP

Jan Kronqvist, David E. Bernal, Andreas Lundell, Ignacio E. Grossmann
2018 Optimization and Engineering  
In this paper, we present a review of deterministic software for solving convex MINLP problems as well as a comprehensive comparison of a large selection of commonly available solvers.  ...  A summary of the most common methods for solving convex MINLP problems is given to better highlight the differences between the solvers.  ...  The authors want to acknowledge the Dagstuhl Seminar 18081 on Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization, which provided valuable insight into the current status of  ... 
doi:10.1007/s11081-018-9411-8 fatcat:qwbcge5wkrdmrp6qww7x3llncu

A Branch and Bound Algorithm for Transmission Network Expansion Planning Using Nonconvex Mixed-Integer Nonlinear Programming Models

Reinaldo T. Zoppei, Marcos A. J. Delgado, Leonardo H. Macedo, Marcos J. Rider, Ruben Romero
2022 IEEE Access  
INDEX TERMS Branch and bound algorithm, mixed-integer nonlinear programming, optimization, transmission network expansion planning. NOMENCLATURE A. FUNCTIONS  ...  for solving this category of problems.  ...  The branch and bound (BB) algorithm, developed by Land and Doig [1] in the 1960s, is a classic method for solving mixed-integer linear programming (MILP) problems.  ... 
doi:10.1109/access.2022.3166153 fatcat:a2xfammw4feefavsoorg2ya2h4

Computational Experience of an Interior-Point SQP Algorithm in a Parallel Branch-and-Bound Framework [chapter]

Eva K. Lee, John E. Mitchell
2000 Applied Optimization  
An interior-point algorithm within a parallel branch-and-bound framework for solving nonlinear mixed integer programs is described.  ...  Preliminary computational results on various classes of linear mixed integer programs and quadratic portfolio problems are presented.  ...  INTRODUCTION Branch-and-bound is a classical approach for solving linear mixed integer programs.  ... 
doi:10.1007/978-1-4757-3216-0_13 fatcat:qvpxsm4ta5ejvmufy57xd5aboi

Undercover Branching [chapter]

Timo Berthold, Ambros M. Gleixner
2013 Lecture Notes in Computer Science  
It explicitly regards the nonlinearity of the problem while branching on integer variables with a fractional relaxation solution.  ...  In this paper, we present a new branching strategy for nonconvex MINLP that aims at driving the created subproblems towards linearity.  ...  For MINLP, solving a (nonconvex) NLP relaxation is already N P-hard.  ... 
doi:10.1007/978-3-642-38527-8_20 fatcat:3ua7qqylkjhvpft2qwpxnxn4ke

Robust subset selection [article]

Ryan Thompson
2020 arXiv   pre-print
This procedure, which we call "robust subset selection" (or "robust subsets"), is defined by a combinatorial optimization problem for which we apply modern discrete optimization methods.  ...  The best subset selection (or "best subsets") estimator is a classic tool for sparse regression, and developments in mathematical optimization over the past decade have made it more computationally tractable  ...  Acknowledgements The author thanks Catherine Forbes and Farshid Vahid for their encouragement and suggestions.  ... 
arXiv:2005.08217v2 fatcat:hs5hu2exuvfezac2osj4fhe2qm

SCIP: global optimization of mixed-integer nonlinear programs in a branch-and-cut framework

Stefan Vigerske, Ambros Gleixner
2017 Optimization Methods and Software  
The most common method to solve nonconvex MINLPs to ε-global optimality is spatial branch-and-bound [54, 57, 62]: recursively divide the original problem into subproblems on smaller domains until the individual  ...  optimization into a single problem class.  ...  This work has been supported by the DFG Research Center MATHEON Mathematics for key technologies in Berlin, the Berlin Mathematical School, and the Research Campus Modal Mathematical Optimization and Data  ... 
doi:10.1080/10556788.2017.1335312 fatcat:3l2viypjinbxtcwadxszfayc3y

Global optimality bounds for the placement of control valves in water supply networks

Filippo Pecci, Edo Abraham, Ivan Stoianov
2018 Optimization and Engineering  
The problem formulation results in a nonconvex mixed integer nonlinear program (MINLP).  ...  Due to its complex mathematical structure, previous literature has solved this nonconvex MINLP using heuristics or local optimization methods, which do not provide guarantees on the global optimality of  ...  This work was supported by the NEC-Imperial Smart Water Systems project, and EPSRC (EP/ P004229/1, Dynamically Adaptive and Resilient Water Supply Networks for a Sustainable Future).  ... 
doi:10.1007/s11081-018-9412-7 fatcat:5hcr6r2esrcnnm3rzx5likef74

A mixed integer disjunctive model for transmission network expansion

L. Bahiense, G.C. Oliveira, M. Pereira, S. Granville
2001 IEEE Transactions on Power Systems  
The mixed integer program is solved by a commercial Branch and Bound code, where an upper bound provided by a heuristic solution is used to reduce the tree search.  ...  Combining the upper bound given by the heuristic and the mixed integer disjunctive model, optimality can be proven for several hard problem instances.  ...  Binato from CEPEL, who developed the GRASP code for transmission planning [10] , which used in this work.  ... 
doi:10.1109/59.932295 fatcat:eqmdzu4po5eblnwahklutdksoy

A Mixed Integer Disjunctive Model for Transmission Network Expansion

L. Bahiense, G. C. Oliveira, M. Pereira, S. Granville
2001 IEEE Power Engineering Review  
The mixed integer program is solved by a commercial Branch and Bound code, where an upper bound provided by a heuristic solution is used to reduce the tree search.  ...  Combining the upper bound given by the heuristic and the mixed integer disjunctive model, optimality can be proven for several hard problem instances.  ...  Binato from CEPEL, who developed the GRASP code for transmission planning [10] , which used in this work.  ... 
doi:10.1109/mper.2001.4311560 fatcat:jdoyyzwxm5b3zldncy4hulj7yq

Extending a CIP Framework to Solve MIQCPs [chapter]

Timo Berthold, Stefan Heinz, Stefan Vigerske
2011 IMA Volumes in Mathematics and its Applications  
This paper discusses how to build a solver for mixed integer quadratically constrained programs (MIQCPs) by extending a framework for constraint integer programming (CIP).  ...  For relaxation, we use an outer approximation generated by linearization of convex constraints and linear underestimation of nonconvex constraints.  ...  Pfetsch for contributing the implementation of the linear outer approximation for second-order cones and Ambros M. Gleixner for his valuable comments on the paper.  ... 
doi:10.1007/978-1-4614-1927-3_15 fatcat:pngauiqh3vfl5g3dzvsje7vyhi
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