Deterministic Global Optimization

Floudas, Christodoulos A.

doi:10.1007/978-1-4757-4949-6

Cited by 421 publications

(139 citation statements)

References 280 publications

(509 reference statements)

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“…The state of the art in the solution methods for this class of problems [2,12,15,19,6] is not at the stage where reasonably sized instances can be solved effectively or reliably. Although the nonconvexity in (P ′ 1 ) is caused by the set of binary products u iv w i j , which can all be linearized exactly in the standard way [7,13], this would imply adding 3 |N| |V | |U| inequality constraints to the formulation.…”

Section: Convex Minlp Reformulationmentioning

confidence: 99%

Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem

2008

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Section: Convex Minlp Reformulationmentioning

confidence: 99%

Optimal configuration of gamma ray machine radiosurgery units: the sphere covering subproblem

2008

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“…In the case of bilevel programming, Vicente (1992), Visweswaran et al (1996), Shimizu et al (1997), Floudas et al (1999), Floudas (2000) and Dempe et al (2005) interpret the optimisation problem as a leader's problem, F, and search for the global minimum of F. The solution point obtained for the follower's problem, f , will respect the stationary (KKT) conditions and hence it can be any stationary point.…”

Section: Global Optimum Of a Bilevel Programming Problemmentioning

confidence: 99%

“…Due to its many applications, multilevel and in particular bilevel programming have evolved significantly. Bilevel programming problems (BLPP) involve a hierarchy of two optimisation problems, of the following form (Vicente and Calamai 1994a;Floudas 2000;Dempe 2003): …”

Section: Introductionmentioning

confidence: 99%

Parametric global optimisation for bilevel programming

et al. 2006

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We propose a global optimisation approach for the solution of various classes of bilevel programming problems (BLPP) based on recently developed parametric programming algorithms. We first describe how we can recast and solve the inner (follower's) problem of the bilevel formulation as a multi-parametric programming problem, with parameters being the (unknown) variables of the outer (leader's) problem. By inserting the obtained rational reaction sets in the upper level problem the overall problem is transformed into a set of independent quadratic, linear or mixed integer linear programming problems, which can be solved to global optimality. In particular, we solve bilevel quadratic and bilevel mixed integer linear problems, with or without right-hand-side uncertainty. A number of examples are presented to illustrate the steps and details of the proposed global optimisation strategy.

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“…There are numerous possible approaches to deriving a tight affine lower bound function from the Bernstein control points of a given polynomial, the convex hull of which is formed in (1). Methods are introduced in [2], [3], [4] and compared in [4].…”

Section: Affine Lower Bound Functionsmentioning

confidence: 99%