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A reformulation framework for global optimization

Journal of global optimization, 2022-05, Vol.57 (1), p.115 [Peer Reviewed Journal]

COPYRIGHT 2022 Springer ;ISSN: 0925-5001 ;EISSN: 1573-2916

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  • Title:
    A reformulation framework for global optimization
  • Author: Lundell, Andreas ; Skjal, Anders ; Westerlund, Tapio
  • Subjects: Algorithms
  • Is Part Of: Journal of global optimization, 2022-05, Vol.57 (1), p.115
  • Description: In this paper, we present a global optimization method for solving nonconvex mixed integer nonlinear programming (MINLP) problems. A convex overestimation of the feasible region is obtained by replacing the nonconvex constraint functions with convex underestimators. For signomial functions single-variable power and exponential transformations are used to obtain the convex underestimators. For more general nonconvex functions two versions of the so-called [alpha]BB-underestimator, valid for twice-differentiable functions, are integrated in the actual reformulation framework. However, in contrast to what is done in branch-and-bound type algorithms, no direct branching is performed in the actual algorithm. Instead a piecewise convex reformulation is used to convexify the entire problem in an extended variable-space, and the reformulated problem is then solved by a convex MINLP solver. As the piecewise linear approximations are made finer, the solution to the convexified and overestimated problem will form a converging sequence towards a global optimal solution. The result is an easily-implementable algorithm for solving a very general class of optimization problems. Keywords Global optimization * Reformulation technique * Convex underestimators * Mixed integer nonlinear programming * Twice-differentiable functions * Signomial functions * Piecewise linear functions * [alpha]BB-underestimator * SGO-algorithm
  • Publisher: Springer
  • Language: English
  • Identifier: ISSN: 0925-5001
    EISSN: 1573-2916
  • Source: ProQuest Central
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