Extended Cutting Plane Algorithm

Still, Claus; Westerlund, Tapio

doi:10.1007/978-0-387-74759-0_168

Cited by 3 publications

(6 citation statements)

References 15 publications

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“…The method was then developed in [15] to cover pseudo-convex MINLP problems. In [11], the convergence properties of both MINLP and NLP problems with quasi-convex constraints were analyzed. The method was further developed in [14] in order to enable the solving of problems consisting of both a pseudo-convex objective function and pseudo-convex constraints.…”

Section: The Extended Cutting Plane Methodsmentioning

confidence: 99%

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Solving a dynamic separation problem using MINLP techniques

Emet

Westerlund

2008

Applied Numerical Mathematics

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Section: The Extended Cutting Plane Methodsmentioning

confidence: 99%

“…s kij M 2 · y kij (11) where M 2 max{s kij }. Hence, if y kij = 0, then s kij = 0, otherwise s kij m kij .…”

Section: Optimization Problem Formulationunclassified

Solving a dynamic separation problem using MINLP techniques

Emet

Westerlund

2008

Applied Numerical Mathematics

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“…From Theorem 2.8, we deduce that this formulation includes the problem considered earlier in [15], where the constraints were pseudoconvex functions.…”

Section: The Generalization Of the αEcp-algorithmmentioning

confidence: 97%

“…Our Nonsmooth α Extended Cutting Plane method (NαECP) solves the problem (P) like αECP, [15] but now the subgradients are used instead of gradients. As in the original αECP method, the nonlinear constraints g j (z) ≤ 0, j = 1, .…”

Section: The Generalized αEcp Algorithmmentioning

confidence: 99%

Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

2013

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In this article, a generalization of the αECP algorithm to cover a class of nondifferentiable Mixed-Integer NonLinear Programming problems is studied. In the generalization constraint functions are required to be f • -pseudoconvex instead of pseudoconvex functions. This enables the functions to be nonsmooth. The objective function is first assumed to be linear but also f • -pseudoconvex case is considered. Furthermore, the gradients used in the αECP algorithm are replaced by the subgradients of Clarke subdifferential. With some additional assumptions, the resulting algorithm shall be proven to converge to a global minimum.

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“…The procedure is repeated until the current iterate is feasible, in which case the iterate is an optimal solution to the original MINLP problem. The original α-ECP algorithm has since been extended to pseudo-convex MINLP optimization problems [28,33,36,38]. It may be observed here that all intermediate MILP problems need not necessarily be solved to optimality, any feasible integer point to the MILP problem may be used to generate new cutting planes as long as the last MILP problem solved is solved to optimality.…”

Section: Introductionmentioning

confidence: 99%

Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm

Still

Westerlund

2005

Comput Optim Applic

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In this article we look at a new algorithm for solving convex mixed integer nonlinear programming problems. The algorithm uses an integrated approach, where a branch and bound strategy is mixed with solving nonlinear programming problems at each node of the tree. The nonlinear programming problems, at each node, are not solved to optimality, rather one iteration step is taken at each node and then branching is applied. A Sequential Cutting Plane (SCP) algorithm is used for solving the nonlinear programming problems by solving a sequence of linear programming problems. The proposed algorithm generates explicit lower bounds for the nodes in the branch and bound tree, which is a significant improvement over previous algorithms based on QP techniques. Initial numerical results indicate that the described algorithm is a competitive alternative to other existing algorithms for these types of problems.

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Extended Cutting Plane Algorithm

Cited by 3 publications

References 15 publications

Solving a dynamic separation problem using MINLP techniques

Solving a dynamic separation problem using MINLP techniques

Extended cutting plane method for a class of nonsmooth nonconvex MINLP problems

Solving Convex MINLP Optimization Problems Using a Sequential Cutting Plane Algorithm

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