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Globally Convergent Cutting Plane Method for Nonconvex Nonsmooth Minimization
Journal of Optimization Theory and Applications, 2010The authors propose an algorithm for solving nonsmooth nonconvex unconstrained programming problems together with some convergence results. This algorithm generates a sequence of interior points of the epigraph of the objective function whose accumulation points are stationary points of the original problem, and so, in case the objective is convex ...
Karmitsa, Napsu +2 more
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On Vaidya's Volumetric Cutting Plane Method for Convex Programming
Mathematics of Operations Research, 1997We describe a simplified and strengthened version of Vaidya's volumetric cutting plane method for finding a point in a convex set 𝒞 ⊂ Rn. At each step the algorithm has a system of linear inequality constraints which defines a polyhedron 𝒫 ⊃ 𝒞, and an interior point x ∈ 𝒫.
K. Anstreicher
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The Cutting-Plane Method for Solving Convex Programs
Journal of the Society for Industrial and Applied Mathematics, 1960J. E. Kelley
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2000
In this chapter, we introduce a class of methods that were among the first to be designed for the solution of integer programming problems. Throughout the past decades, however, computational evidence has revealed that cutting planes, while appealing from a theoretical point of view, do not appear to work very well if applied to general integer ...
H. A. Eiselt, C.-L. Sandblom
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In this chapter, we introduce a class of methods that were among the first to be designed for the solution of integer programming problems. Throughout the past decades, however, computational evidence has revealed that cutting planes, while appealing from a theoretical point of view, do not appear to work very well if applied to general integer ...
H. A. Eiselt, C.-L. Sandblom
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2014
Subgradient methods described in the previous chapter use only one arbitrary subgradient (generalized gradient) at a time, without memory of past iterations. If the information from previous iterations is kept, it is possible to define a model—the so-called cutting plane model—of the objective function.
Adil Bagirov +2 more
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Subgradient methods described in the previous chapter use only one arbitrary subgradient (generalized gradient) at a time, without memory of past iterations. If the information from previous iterations is kept, it is possible to define a model—the so-called cutting plane model—of the objective function.
Adil Bagirov +2 more
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IEEE Robotics and Automation Letters
Laminectomy represents an effective surgical procedure for the treatment of lumbar spinal stenosis. Due to the intricate anatomical structure of the lumbar spine, meticulous surgical path planning is essential to ensure the safety of the procedure and ...
Gaodeng Liu +6 more
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Laminectomy represents an effective surgical procedure for the treatment of lumbar spinal stenosis. Due to the intricate anatomical structure of the lumbar spine, meticulous surgical path planning is essential to ensure the safety of the procedure and ...
Gaodeng Liu +6 more
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Probabilistic analytic center cutting plane method with multiple cuts
2014 European Control Conference (ECC), 2014A probabilistic analytic center cutting plane method with multiple cuts is proposed for a class of robust feasibility problems which is to find a solution satisfying a set of parameter dependent convex constraints for all possible parameter values. In particular, a new update rule is presented for constructing a smaller polytope which contains the ...
Takayuki Wada, Yasumasa Fujisaki
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Cutting-Plane Methods without Nested Constraint Sets
Operations Research, 1970This paper gives general conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the sub-problems be sequentially nested. Conditions are given under which inactive constraints may be dropped after each subproblem.
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LLMs for Cold-Start Cutting Plane Separator Configuration
arXiv.orgMixed integer linear programming (MILP) solvers expose hundreds of parameters that have an outsized impact on performance but are difficult to configure for all but expert users.
Connor Lawless +4 more
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Polynomial Interior Point Cutting Plane Methods
Optimization Methods and Software, 2003Polynomial cutting plane methods based on the logarithmic barrier function and on the volumetric center are surveyed. These algorithms construct a linear programing relaxation of the feasible region, find an appropriate approximate center of the region, and call a separation oracle at this approximate center to determine whether additional constraints ...
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