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On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming [article]

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2019 arXiv   pre-print
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global epsilon-optimality with spatial branch and bound is a tight, computationally tractable relaxation.  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  The authors thank the Schloss Dagstuhl -Leibniz Center for Informatics for hosting the Seminar 18081 "Designing and Implementing Algorithms for Mixed-Integer Nonlinear Optimization" for providing the environment  ... 
arXiv:1912.00356v1 fatcat:f3hmuz6vajb23pp2apnd4sdc4a

On Generalized Surrogate Duality in Mixed-Integer Nonlinear Programming [chapter]

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2020 Lecture Notes in Computer Science  
The most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global -optimality with spatial branch and bound is a tight, computationally tractable relaxation.  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  In this paper, we revisit surrogate duality in the context of mixed-integer nonlinear programming.  ... 
doi:10.1007/978-3-030-45771-6_25 fatcat:hrxrj7tnb5bo3e2xiai5jx4tfm

On generalized surrogate duality in mixed-integer nonlinear programming

Benjamin Müller, Gonzalo Muñoz, Maxime Gasse, Ambros Gleixner, Andrea Lodi, Felipe Serrano
2021 Mathematical programming  
AbstractThe most important ingredient for solving mixed-integer nonlinear programs (MINLPs) to global $$\epsilon $$ ϵ -optimality with spatial branch and bound is a tight, computationally tractable relaxation  ...  These relaxations were actively studied for linear integer programs in the 70s and 80s, but they have been scarcely considered since.  ...  Surrogate duality in MINLPs While surrogate duality in its broader definition can be applied to any MINLP, to the best of our knowledge, only mixed-integer linear programming problems have been considered  ... 
doi:10.1007/s10107-021-01691-6 fatcat:hbch5fhng5fzdoahbie7z4zpu4

Page 4148 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
I. (2-KIEV) Duality relations and conditions for optimality in nonlinear stochastic programming problems. (Russian) Issled. Operatsii i ASU No. 31 (1988), 19-22, 112.  ...  Summary: “In this note we point out that a constraint generation scheme can be used successfully in connection with surrogate relaxation.  ... 

Page 891 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
Surrogate duality in a branch-and-bound procedure. Naval Res. Logist. Quart. 28 (1981), no. 1, 93-101.  ...  Author’s summary: “We consider a solution algorithm for a nonlinear integer programming problem with a monotonically increasing target function and constraints specified in the form of a nonlinear function  ... 

Page 7151 of Mathematical Reviews Vol. , Issue 89M [page]

1989 Mathematical Reviews  
{For the entire collection see MR 89g:90005.} 89m:90116 90C10 90C11 Ram, Balasubramanian (1-NCAT); Karwan, Mark H. (1-SUNYB) A result in surrogate duality for certain integer programming problems.  ...  However, for such surrogate formulations, when the variables are mixed-integer, the primal- dual gap may not be zero.  ... 

Page 353 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
of Lagrangian duality in integer programming.  ...  types of mixed integer linear assignment problems.  ... 

Page 3359 of Mathematical Reviews Vol. , Issue 98E [page]

1998 Mathematical Reviews  
It is also shown that this bound on coordination steps also applies to a reformulation of the above general nonlinear problem.”  ...  in modern codes such as the CPLEX mixed 0-1 integer programming solver.” 98e:90096 90C09 90C27 Pferschy, Ulrich (A-GRAZ-OR; Graz); Pisinger, David (DK-CPNH-C; Copenhagen); Woeginger, Gerhard J.  ... 

Duality in Optimization and Constraint Satisfaction [chapter]

J. N. Hooker
2006 Lecture Notes in Computer Science  
A general analysis of duality can also unify some existing solution methods and suggest new ones.  ...  in the type of inference on which they are based.  ...  Both of these strategies have long been used in linear programming, for example. They can be applied to integer and mixed integer programming as well [6] .  ... 
doi:10.1007/11757375_3 fatcat:ve3xmr3ibjf27iifhokmmpot6e

Network-Constrained Day-Ahead Auction for Consumer Payment Minimization

Ricardo Fernandez-Blanco, Jose M. Arroyo, Natalia Alguacil
2014 IEEE Transactions on Power Systems  
This transformation relies on the application of results from duality theory of linear programming and integer algebra.  ...  The resulting mixed-integer linear bilevel program is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software.  ...  In [22] , the nonlinear KKT-based MPEC presented in [18] was converted to a mixed-integer linear program by using additional binary variables.  ... 
doi:10.1109/tpwrs.2013.2284283 fatcat:njtjnhbeezfkfci6p4kvompm4m

Network-constrained day-ahead auction for consumer payment minimization

Ricardo Fernandez-Blanco, Jose Arroyo, Natalia Alguacil
2014 2014 IEEE PES General Meeting | Conference & Exposition  
This transformation relies on the application of results from duality theory of linear programming and integer algebra.  ...  The resulting mixed-integer linear bilevel program is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software.  ...  In [22] , the nonlinear KKT-based MPEC presented in [18] was converted to a mixed-integer linear program by using additional binary variables.  ... 
doi:10.1109/pesgm.2014.6938821 fatcat:qmhsfjvslbflfa74oedi5w56vq

Lagrangian relaxation neural networks for job shop scheduling

P.B. Luh, Xing Zhao, Yajun Wang, L.S. Thakur
2000 IEEE Transactions on Robotics and Automation  
The convergence of the network is proved, and a general framework for neural implementation is established, allowing creative variations.  ...  When applying the network for job shop scheduling, the separability of problem formulation is fully exploited, and a new neuron-based dynamic programming is developed making innovative use of the subproblem  ...  LRNN FOR SEPARABLE INTEGER PROGRAMMING PROBLEMS A. LR for Integer Programming Integer programming problems are generally difficult to solve because of their inherent combinatorial complexity.  ... 
doi:10.1109/70.833193 fatcat:o4ljmcwidrbxtmamidyw4q6sdm

Page 812 of Mathematical Reviews Vol. , Issue 2000a [page]

2000 Mathematical Reviews  
The approach can be applied to multi-stage problems with mixed-integer variables in each time stage. Numerical results are presented for some two- stage test problems.” Th. M.  ...  Summary: “We present an algorithm for solving stochastic integer programming problems with recourse, based on a dual decompo- sition scheme and Lagrangian relaxation.  ... 

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 the augmented Lagrangian dual for integer programming

N. L. Boland, A. C. Eberhard
2014 Mathematical programming  
We are able to show that the penalty parameter applied to the augmented Lagrangian term may be placed at a fixed, large value and still obtain strong duality for pure integer programs.  ...  As a corollary, we obtain proof that the augmented Lagrangian is a strong dual for integer programming.  ...  the technique of column generation -undoubtedly one of the success stories of integer programming [8] .  ... 
doi:10.1007/s10107-014-0763-3 fatcat:h6axqeucabfpti3z5eogl3d33m
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