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An algorithm for nonlinear optimization problems with binary variables

2008
*
Computational optimization and applications
*

One of the challenging

doi:10.1007/s10589-008-9218-1
fatcat:uj62ggkkczc2bmgygvhf4uv5fe
*optimization**problems*is determining the minimizer of a*nonlinear*programming*problem*that has*binary**variables*. ... Any such*problem**with*bounded discrete*variables*, especially*binary**variables*, may be transformed to that of finding a global optimum of a*problem*in continuous*variables*. ...*nonlinear**optimization**problems**with**binary**variables*. ...##
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Computational experience with dicopt solving MINLP problems in process systems engineering

1989
*
Computers and Chemical Engineering
*

This paper discusses

doi:10.1016/0098-1354(89)85008-2
fatcat:fitw5sah35gmldwgtjaj7z74i4
*an*implementation of the Outer-Approximation/Equality -Relaxation*algorithm**for*solving MINLP*problems*that arise in process systems engineering. ... Computational experience in solving fifteen MINLP*problems**with*DICOPT is reported. ... Computer times on*an*IBM-3090/600 are typically of the order of only 2-100 seconds*for**problems**with*up to 60 0-1*variables*and 410*variables*and constraints. ...##
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Predictive Control of Nonlinear Hybrid Systems Using Generalized Outer Approximation

2008
*
IFAC Proceedings Volumes
*

This paper presents

doi:10.3182/20080706-5-kr-1001.00612
fatcat:pwb6zee5wvb2lk5n2ruuigxmri
*an*efficient*optimization**algorithm**for*mixed integer*nonlinear*programming (MINLP)*problem*resulting from multiple partially linearized (MPL) model based control of*nonlinear*hybrid ... The*algorithm*uses structural information of the canonical MPL framework and derives comparatively easier quadratic programming (QP) primal*problem*as well as*an*MILP master*problem**for*generalized outer ... The master*problem*results in*an*MILP whose solution is a lower bound of the MINLP. The master*problem*also produces the value of the*binary**variables**for*next iteration. ...##
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A Review of Piecewise Linearization Methods

2013
*
Mathematical Problems in Engineering
*

*for*obtaining

*an*approximated global

*optimal*solution. ... How to locate a global

*optimal*solution of a

*nonlinear*programming

*problem*is

*an*important issue in

*optimization*theory. ... Developing

*an*efficient polynomial time

*algorithm*

*for*solving nonconvex

*problems*by piecewise linearization techniques is still a challenging question. ...

##
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Global optimization of MINLP problems in process synthesis and design

1997
*
Computers and Chemical Engineering
*

it allows to solve the underestimating

doi:10.1016/s0098-1354(97)87542-4
fatcat:iqgiswkqdrfvreg6s5ygc7isra
*problems*to global*optimality*using the GBD*algorithm*or the OA*algorithm*, provided that the*binary**variables*participate separably and linearly. ... The conditions imposed on the functionality of the*binary**variables*differ*for*each method : linear and mixed bilinear terms can be treated*with*the SMIN-BB; mixed*nonlinear*terms whose continuous relaxation ... and not necessarily separable*binary**variables*; the Generalized Benders Decomposition*algorithm*, GBD (Geoffrion, 1972; Floudas et al., 1989) , is designed*for**problems**with*a convex continuous part and ...##
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Global Optimization of MINLP Problems in Process Synthesis and Design

1997
*
Computers and Chemical Engineering
*

it allows to solve the underestimating

doi:10.1016/s0098-1354(97)00089-6
fatcat:miaj3o2omfdblh4r5g6ecp6pkm
*problems*to global*optimality*using the GBD*algorithm*or the OA*algorithm*, provided that the*binary**variables*participate separably and linearly. ... The conditions imposed on the functionality of the*binary**variables*differ*for*each method : linear and mixed bilinear terms can be treated*with*the SMIN-BB; mixed*nonlinear*terms whose continuous relaxation ... and not necessarily separable*binary**variables*; the Generalized Benders Decomposition*algorithm*, GBD (Geoffrion, 1972; Floudas et al., 1989) , is designed*for**problems**with*a convex continuous part and ...##
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Inverse kinematics of binary manipulators by using the continuous-variable-based optimization method

2006
*
IEEE Transactions on robotics
*

The key idea of the proposed method is to formulate the inverse kinematics

doi:10.1109/tro.2005.858864
fatcat:ihjpxqk25vbgndew5amt3uhpji
*problem*of a*binary*manipulator as*an**optimization**problem**with*real design*variables*, in which the real*variables*are forced ... In this case, numerically efficient inverse kinematics*algorithms**for**binary*manipulators usually require impractically large memory size*for*the real-time calculation of the*binary*states of all joints ... ACKNOWLEDGMENT The authors appreciate discussions*with*Prof. F. C. Park at Seoul National University during this investigation. ...##
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Relaxation strategy for the structural optimization of process flow sheets

1987
*
Industrial & Engineering Chemistry Research
*

This paper presents

doi:10.1021/ie00069a026
fatcat:meftt2gvqfagjduytpuwh32dke
*an*Equality Relaxation variant to the Outer-Approximation*algorithm**for*solving mixed-integer*nonlinear*programming (MINLP)*problems*that arise in structural*optimization*of process ... The proposed*algorithm*has the important capability of being able to explicitly handle*nonlinear*equations within MINLP formulations that have linear integer*variables*and linear/*nonlinear*continuous*variables*... the*optimal*value of the*binary**variables*. ...##
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Reformulations and algorithms for the optimization of switching decisions in nonlinear optimal control

2009
*
Journal of Process Control
*

In model-based

doi:10.1016/j.jprocont.2009.03.008
fatcat:uza4dupvnzaanghamyc6piyrpa
*nonlinear**optimal*control switching decisions that can be*optimized*often play*an*important role. ...*Optimization**algorithms*need to take the discrete nature of the*variables*that model these switching decisions into account. ... We introduce*an*additional*variable*, e.g.,*for*ω i (t) · ω j (t): ω ij (t) := 1 if ω i (t) = ω j (t) = 1 0 else The new*binary**variables*can be incorporated into the*optimization**problem*by adding the ...##
###
Page 7919 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

Summary: “ELSO is

*an*environment*for*the solution of large-scale*optimization**problems*.*With*ELSO the user is required to provide only a code*for*the evaluation of a partially separable function. ... It has been shown recently that some properties of the maximum weight stable set*problem*hold true in the more general setting of*binary*integer programs*with*two*variables*per inequality. ...##
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Real-coded genetic algorithm for system identification and controller tuning

2009
*
Applied Mathematical Modelling
*

In the proposed genetic

doi:10.1016/j.apm.2008.11.006
fatcat:iaxqvwmns5ad5clkb3ei4cbvne
*algorithm*, the*optimization**variables*are represented as floating point numbers. ... This paper presents*an*application of real-coded genetic*algorithm*(RGA)*for*system identification and controller tuning in process plants. ... In this work the*problem*of controller tuning is formulated as*an**optimization**problem*. ...##
###
Symmetry-exploiting cuts for a class of mixed-0/1 second-order cone programs

2014
*
Discrete Optimization
*

We will analyze mixed-0/1 second-order cone programs where the continuous and

doi:10.1016/j.disopt.2014.04.002
fatcat:tmaguogruzcibn5kbwbj5xyah4
*binary**variables*are solely coupled via the conic constraints. ...*For*example in [7] lift-and-project based cuts*for*mixed 0/1 conic programming*problems*have been studied. ... ACKNOWLEDGEMENTS The authors are indebted to the two anonymous referees*for*the helpful comments. ...##
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Nonlinear Model-Based Process Operation under Uncertainty Using Exact Parametric Programming

2017
*
Engineering
*

In the present work, two new, (multi-)parametric programming (mp-P)-inspired

doi:10.1016/j.eng.2017.02.008
fatcat:c3wzwbusenbatlrgmllcvrnnru
*algorithms**for*the solution of mixed-integer*nonlinear*programming (MINLP)*problems*are developed,*with*their main focus being ...*For*p-MINLP, the solution is given by*an**optimal*solution as*an*explicit function of the uncertain parameters. ... Compliance*with*ethics guidelines Vassilis M. Charitopoulos, Lazaros G. Papageorgiou, and Vivek Dua declare that they have no conflict of interest or financial conflicts to disclose. ...##
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Convex separable optimization is not much harder than linear optimization

1990
*
Journal of the ACM
*

This paper presents a general-purpose

doi:10.1145/96559.96597
fatcat:lkqrg236dvfzhjcxkn5umtet4u
*algorithm**for*converting procedures that solves linear programming*problems**with*or without integer*variables*, to procedures*for*solving the respective*nonlinear*separable ...*An**algorithm**for*finding*an*c-accurate*optimal*continuous solution to the*nonlinear**problem*that is polynomial in log( l/c) and the input size and the largest subdeterminant of the constraint matrix is ... The authors are grateful to Ilan Adler*for*several stimulating discussions that motivated the work done in this paper. ...##
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MINLP OPTIMIZATION OF STEEL FRAMES
[chapter]

2007
*
Volume 3 Number 3
*

The Modified Outer-Approximation/ Equality-Relaxation

doi:10.18057/ijasc.2007.3.3.5
fatcat:dzpztz3qyfg5vaxfwtsfl6sevi
*algorithm*and a two-phase MINLP*optimization*approach were applied*for*the*optimization*. ... It performs the discrete*optimization*of discrete decisions simultaneously*with*the continuous*optimization*of continuous parameters. ... The MILP*optimization*master*problem*predicts a new vector of*binary**variables*. ...
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