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An Outer-Inner Approximation for Separable Mixed-Integer Nonlinear Programs

Hassan Hijazi, Pierre Bonami, Adam Ouorou
2014 INFORMS journal on computing  
A common structure in convex mixed-integer nonlinear programs (MINLPs) is separable nonlinear functions.  ...  The first improvement is a simple extended formulation, the second is a refined outer approximation, and the third is a heuristic inner approximation of the feasible region.  ...  Acknowledgments The authors thank Jeff Linderoth and Mustafa Kılınç for sharing the UFL and SSSD instances with us.  ... 
doi:10.1287/ijoc.1120.0545 fatcat:bdpadkeu5zgazlpnht5sxafpqm

Page 3876 of Mathematical Reviews Vol. , Issue 84i [page]

1984 Mathematical Reviews  
If any method can be used without changes to solve mixed integer nonlinear programming problems, that fact is mentioned in the description of the algorithm.  ...  Cooper, Mary W.(1-SMU) 84i:90126 A survey of methods for pure nonlinear integer programming. Management Sci. 27 (1981), no. 3, 353-361.  ... 

Extended Formulations in Mixed-integer Convex Programming [article]

Miles Lubin and Emre Yamangil and Russell Bent and Juan Pablo Vielma
2015 arXiv   pre-print
We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP).  ...  For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations  ...  An outer-approximation algorithm for mixed-integer conic programming Although the conic representation (MICONE) does not preclude the use of derivative-based solvers for continuous relaxations, derivative-based  ... 
arXiv:1511.06710v1 fatcat:csbh77daivasncpbsnodb7ay44

A comparative study of SQP-type algorithms for nonlinear and nonconvex mixed-integer optimization

Oliver Exler, Thomas Lehmann, Klaus Schittkowski
2012 Mathematical Programming Computation  
We present numerical results of a comparative study of codes for nonlinear and nonconvex mixed-integer optimization.  ...  The underlying algorithms are based on sequential quadratic programming (SQP) with stabilization by trust-regions, linear outer approximations, and branch-and-bound techniques.  ...  Another frequently used solution method for solving mixed-integer nonlinear programming problems is based on linear outer approximations.  ... 
doi:10.1007/s12532-012-0045-0 fatcat:og2s7nejq5hzrkfez2ob4mtfbi

A review of recent advances in global optimization

C. A. Floudas, C. E. Gounaris
2008 Journal of Global Optimization  
It covers the areas of twice continuously differentiable nonlinear optimization, mixed-integer nonlinear optimization, optimization with differential-algebraic models, semi-infinite programming, optimization  ...  This paper presents an overview of the research progress in deterministic global optimization during the last decade (1998)(1999)(2000)(2001)(2002)(2003)(2004)(2005)(2006) (2007) (2008).  ...  are mixed integer nonlinear in the outer variables and linear, polynomial, or multilinear in the inner integer variables, and linear in inner continuous variables; and applied it to several challenging  ... 
doi:10.1007/s10898-008-9332-8 fatcat:72fpfq72hrdzhf6mxqyc6ssezm

An outer approximation algorithm for multi-objective mixed-integer linear and non-linear programming [article]

Fritz Bökler, Sophie N. Parragh, Markus Sinnl, Fabien Tricoire
2022 arXiv   pre-print
In this paper, we present the first outer approximation algorithm for multi-objective mixed-integer linear programming problems with any number of objectives.  ...  non-dominated extreme points in the case of multiobjective mixed-integer programming (MOMILP).  ...  For the purpose of open access, the author has applied a CC BY public copyright licence to any Author Accepted Manuscript version arising from this submission.  ... 
arXiv:2103.16647v2 fatcat:7d4rbvhbifhv7pv57rayzvrktm

Using Interior-Point Methods within an Outer Approximation Framework for Mixed Integer Nonlinear Programming [chapter]

Hande Y. Benson
2011 IMA Volumes in Mathematics and its Applications  
that arise in the solution of mixed-integer nonlinear programming problems via outer approximation.  ...  The generality of this approach to handle any change to the problem makes it suitable for the outer approximation framework, where each nonlinear subproblem can differ from the others in the sequence in  ...  Outer approximation. The Outer Approximation (OA) algorithm solves an alternating sequence of NLPs and mixed-integer linear programming problems (MILPs) to solve (1.1).  ... 
doi:10.1007/978-1-4614-1927-3_7 fatcat:ewip4pylxjdzjgvtq34okwxxim

Solving mixed integer nonlinear programs by outer approximation

Roger Fletcher, Sven Leyffer
1994 Mathematical programming  
Duran and Grossmann (1986) suggest an outer approximation scheme for solving a class of MINLPs that are linear in the integer variables by a nite sequence of relaxed MILP master programs and NLP subproblems  ...  The worst case performance of the outer approximation algorithm is investigated and an example is given for which it visits all integer assignments.  ...  Introduction Many optimization problems involve integer or discrete variables and can be modelled as Mixed Integer Nonlinear Programming problems (MINLPs).  ... 
doi:10.1007/bf01581153 fatcat:fbfqws26ozbphk76vobermnrtm

Global optimization of mixed-integer nonlinear programs: A theoretical and computational study

Mohit Tawarmalani, Nikolaos V. Sahinidis
2004 Mathematical programming  
This work addresses the development of an efficient solution strategy for obtaining global optima of continuous, integer, and mixed-integer nonlinear programs.  ...  We present computational experience with benchmark separable concave quadratic programs, fractional 0-1 programs, and mixed-integer nonlinear programs from applications in synthesis of chemical processes  ...  Mixed-integer nonlinear programs from minlplib In this section, we address the solution of mixed-integer nonlinear programs.  ... 
doi:10.1007/s10107-003-0467-6 fatcat:cl7justhpnbm5b4r7u5cphh2ky

On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control [chapter]

Michael N. Jung, Christian Kirches, Sebastian Sager
2013 Facets of Combinatorial Optimization  
In this article we give an overview over a variety of different modeling approaches, including outer versus inner convexification, generalized disjunctive programming, and vanishing constraints.  ...  Logical implications appear in a number of important mixed-integer nonlinear optimal control problems (MIOCPs).  ...  Disjunctive Programming Based on the work of Balas for integer linear programs, Grossmann and coworkers developed Generalized Disjunctive Programming (GDP) for mixed-integer nonlinear programs [30] .  ... 
doi:10.1007/978-3-642-38189-8_16 fatcat:h7ykdvpiafeszn3ycgqpxdhxue

Exact Mixed-integer Convex Programming Formulation for Optimal Water Network Design [article]

Byron Tasseff, Russell Bent, Marina A. Epelman, Donatella Pasqualini, Pascal Van Hentenryck
2020 arXiv   pre-print
In this paper, it is shown that, in fact, the original mixed-integer nonconvex program can be reformulated exactly as an MICP.  ...  Using this novel MICP as a foundation, a global optimization algorithm is developed, leveraging heuristics, outer approximations, and feasibility cutting planes for infeasible designs.  ...  Noname; manuscript no. 00-0000-0000.00 13 Tasseff et al.: Exact Mixed-integer Convex Programming Formulation for Optimal Water Network Design Tasseff et al.: Exact Mixed-integer Convex Programming  ... 
arXiv:2010.03422v1 fatcat:sbj3hx33bzanvbfrpaiusg5f2y

Bilevel programming model and solution method for mixed transportation network design problem

Haozhi Zhang, Ziyou Gao
2009 Journal of Systems Science and Complexity  
By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level  ...  Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem.  ...  Therefore, the mixed-integer bilevel programming model for MNDP can be transformed into an equivalent single-level nonlinear optimization problem.  ... 
doi:10.1007/s11424-009-9177-3 fatcat:vdud3cyttfdktkgwrknyqxosgm

Convex integer optimization with Frank-Wolfe methods [article]

Deborah Hendrych and Hannah Troppens and Mathieu Besançon and Sebastian Pokutta
2022 arXiv   pre-print
outer approximation scheme.  ...  Mixed-integer nonlinear optimization is a broad class of problems that feature combinatorial structures and nonlinearities.  ...  ., 2022) and Pavito.jl (JuMP-dev, 2018 ) use single-tree polyhedral outer approximation approaches, relying on the Mixed-Integer Programming (MIP) solver to build the main relaxation of the problem.  ... 
arXiv:2208.11010v2 fatcat:voozs6z3cff6bchp5ijucvcc24

Page 6034 of Mathematical Reviews Vol. , Issue 87j [page]

1987 Mathematical Reviews  
Summary: “In a recent paper some duality results were proved for a pair of nonsymmetric and nonlinear mixed integer program- ming problems under pseudoconvexity/pseudoconcavity, separa- bility and an additional  ...  [Nanda, Sudarsan] (6-IITKH); Acharya, D. (6-IITKH) A note on a pair of nonlinear mixed integer programming problems. European J. Oper. Res. 28 (1987), no. 1, 89-92.  ... 

Page 4625 of Mathematical Reviews Vol. , Issue 97G [page]

1997 Mathematical Reviews  
The paper is devoted to stochastic programming problems with a complete (fixed) mixed-integer recourse.  ...  Under an approximation criterion for 90C Mathematical programming 972:90098 computing the saddle point the proposed algorithm gives global convergence.  ... 
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