A sequential cutting plane algorithm for solving convex NLP problems

Still, Claus; Westerlund, Tapio

doi:10.1016/j.ejor.2005.02.045

Cited by 8 publications

(7 citation statements)

References 6 publications

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“…Contrary to [6] and [26], which both use an SQP solver for solving the NLP subproblems, we use an NLP version of the Sequential Cutting Plane algorithm, described in [34], to solve the NLP subproblems. The difference from the SQP approach is that we solve a sequence of LP problems rather than QP problems in order to find a solution to the NLP subproblem.…”

Section: Solving Nlp Subproblemsmentioning

confidence: 99%

“…The NLP version of the SCP algorithm, [34], solves the NLP problem (NLP k ) to optimality by doing a sequence of NLP iterations. In each NLP iteration, a sequence of LP subiterations is performed.…”

Section: Overview Of the Scp Algorithm For Nlp Problemsmentioning

confidence: 99%

“…Convergence to an optimal solution for the MINLP problem can be ensured by the fact that the branch and bound tree is finite and by us having shown earlier, [34], that the NLP part of the algorithm converges to an optimal solution.…”

Section: Convergence To An Optimal Solutionmentioning

confidence: 99%

“…The SCP algorithm has been implemented in MATLAB using the implementation of the NLP version described in [34] as the base for solving the NLP problems in each node. SOS1 branching, introduced in [2], was implemented in the algorithm as well as several heuristics to improve convergence.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…The technique differs from the α-ECP method, where the generation of cutting planes is separated from the branching process. For the NLP subproblems, we solve a sequence of linear programming (LP) problems utilizing ideas from [34] in contrast to the algorithm in [26], which is based on the filterSQP method [14,15]. The filterSQP method solves a sequence of QP problems in order to solve the NLP subproblems.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Solving Nlp Subproblemsmentioning

confidence: 99%

Section: Overview Of the Scp Algorithm For Nlp Problemsmentioning

confidence: 99%

Section: Convergence To An Optimal Solutionmentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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