On linear programming relaxations for solving polynomial programming problems

Dalkiran, Evrim; Ghalami, Laleh

doi:10.1016/j.cor.2018.06.010

Cited by 5 publications

(5 citation statements)

References 38 publications

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“…For instance, Mevissen and Kojima (2010) proposed four heuristics for the iterative transformation of a POP into a QCP, which differ in the criterion used for substitution variable selection and the extent of substitution in each iteration, with a view to introducing as few auxiliary variables as possible. Similarly, Dalkiran and Ghalami (2018) considered three QCP reformulation schemes that differ in the number of auxiliary variables and constraints.…”

Section: Monomial Decomposition Algorithmmentioning

confidence: 99%

“…Further work on minimizing the number of additional variables while maintaining the sparsity of the equivalent QCP was conducted by Mevissen and Kojima (2010), who compared different algorithms with a view to constructing tight SDP relaxations of POPs. More recently, Dalkiran and Ghalami (2018) analyzed the strength and computational efficiency of polyhedral relaxations of POPs derived from three QCP reformulation strategies introducing more or less auxiliary variables and constraints.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Assessment of a two-step approach for global optimization of mixed-integer polynomial programs using quadratic reformulation

Karia

Adjiman²,

Chachuat³

2022

Computers & Chemical Engineering

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Section: Monomial Decomposition Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of a two-step approach for global optimization of mixed-integer polynomial programs using quadratic reformulation

Karia

Adjiman²,

Chachuat³

2022

Computers & Chemical Engineering

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“…Algorithms with linearization techniques were built to reformulate polynomial programs with objective functions and constraint functions that are polynomial specific [3] then Dalkiran and Sherali carried out another strategy to solve polynomial programs through the process of filtering the RLT bound-constraint factors [4]. Furthermore, Dalkiran continued his research by using linear program relaxation to solve polynomial programs [5].…”

Section: Introductionmentioning

confidence: 99%

Convex Relaxation for Solving Polynomial Programs through Quadratization Technique

Sinaga,

Tulus,

Herawati

et al. 2024

Construction Technologies and Architecture

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In this paper, we study convex quadratic relaxation in polynomial programming. The goal is to solve polynomial programs through quadratic reformulation with the factorization method. The quadratization of monomials of degree more than two is carried out by replacing each pair of factors of the monomial with auxiliary variables. In this paper, each pair of factors of a monomial will be considered. The quadratic program obtained is convexified by using eigenvalues. As a result, the quadratic reformulation involving all factors of the monomial strengthens the information of the polynomial function but increases the dimensionality of the variables significantly. The next work is to develop a strategy to reduce the dimensions of the auxiliary variables.

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“…Such techniques have been used in continuous polynomial optimization, as in RLT-POS and further developments [9,8], and more recently as the base relaxation in a solver called RAPOSa [19]. In the case of binary variables, Hojny, Pfetsch and Walter [20] use such an approach to tackle BPO.…”

Section: Introductionmentioning

confidence: 99%