Global Optimization Issues in Multiparametric Continuous and Mixed-Integer Optimization Problems

Dua, Vivek; Papalexandri, Katerina P.; Pistikopoulos, E.N.

doi:10.1023/b:jogo.0000049091.73047.7e

Cited by 75 publications

(21 citation statements)

References 39 publications

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“…Current research focus is towards general non-linear models, for which recent results on global multi-parametric programming (Dua et al 2004) can be used; and general dynamic multi-level problems, for which a dynamic programming approach coupled with parametric programming can be applied (Faísca et al 2007a). …”

Section: Discussionmentioning

confidence: 99%

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A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

et al. 2007

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In this paper, we outline the foundations of a general global optimisation strategy for the solution of multilevel hierarchical and general decentralised multilevel problems, based on our recent developments on multi-parametric programming and control theory. The core idea is to recast each optimisation subproblem, present in the hierarchy, as a multi-parametric programming problem, with parameters being the optimisation variables belonging to the remaining subproblems. This then transforms the multilevel problem into single-level linear/convex optimisation problems. For decentralised systems, where more than one optimisation problem is present at each level of the hierarchy, Nash equilibrium is considered. A three person dynamic optimisation problem is presented to illustrate the mathematical developments.

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Section: Discussionmentioning

confidence: 99%

“…For the sake of clarity, the methodology is described using formulations with quadratic cost functions and linear constraints, however, it is applicable to general non-linear problems using suitable multi-parametric programming algorithms (Dua et al 2004). …”

Section: Proposed Methodologymentioning

confidence: 99%

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

et al. 2007

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“…Degenerate solutions are avoided. mp-NLP Dua et al [97]; Dua et al [99] Non-convex optimization. Generate convex overestimator and underestimator.…”

Section: Multi-parametric Moving Horizon Policiesmentioning

confidence: 99%

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Diangelakis

Pistikopoulos

2017

Computer Aided Chemical Engineering

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“…In terms of numerical and theoretical results of parameterized QIPs, an early computational study by McBride and Yormark [41] considers a sequence of 0-1 QIPs parameterized over the right-hand side of a single constraint. More recently, Dua et al [20] develops a global optimization algorithm for solving a general class of nonconvex mixed-integer programs parameterized over the right-hand sides of a set of possibly nonlinear constraints. Their proposed algorithmic approach utilizes convex under-and over-estimators within a generic branch-and-bound algorithm.…”

Section: Quadratic Integer Programmingmentioning

confidence: 99%

Two-stage quadratic integer programs with stochastic right-hand sides

2010

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We consider two-stage quadratic integer programs with stochastic righthand sides, and present an equivalent reformulation using value functions. We propose a two-phase solution approach. The first phase constructs value functions of quadratic integer programs in both stages. The second phase solves the reformulation using a global branch-and-bound algorithm or a level-set approach. We derive some basic properties of value functions of quadratic integer programs and utilize them in our algorithms. We show that our approach can solve instances whose extensive forms are hundreds of orders of magnitude larger than the largest quadratic integer programming instances solved in the literature.Keywords Stochastic integer programming · Quadratic integer programming · Value functions · Superadditive duality Mathematics Subject Classification (2000) 90C15 · 90C20 · 90C26 · 90C31

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Global Optimization Issues in Multiparametric Continuous and Mixed-Integer Optimization Problems

Cited by 75 publications

References 39 publications

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

A multi-parametric programming approach for multilevel hierarchical and decentralised optimisation problems

Model-based multi-parametric programming strategies towards the integration of design, control and operational optimization

Two-stage quadratic integer programs with stochastic right-hand sides

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