Primal-dual-infeasible Newton approach for the analytic center deep-cutting plane method

DOI10.1023/A:1021714926231zbMath0948.90149OpenAlexW104293380MaRDI QIDQ1293951

K. Appert

Publication date: 15 September 1999

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1021714926231

zbMATH Keywords

complexityanalytic centersconvergenceconvex feasibilitycutting plane algorithmdeep cutsprimal dual-infeasible Newton methodprimal-dual column generation

Mathematics Subject Classification ID

Polyhedral combinatorics, branch-and-bound, branch-and-cut (90C57) Methods of quasi-Newton type (90C53)

Related Items (4)

A \(J\)-symmetric quasi-Newton method for minimax problems ⋮ A cutting plane method for solving KYP-SDPs ⋮ Specialized fast algorithms for IQC feasibility and optimization problems. ⋮ Enhancing the behavior of interior-point methods via identification of variables

Cites Work

• Karmarkar's algorithm and the ellipsoid method
• Solving combinatorial optimization problems using Karmarkar's algorithm
• A new polynomial time method for a linear complementarity problem
• On the complexity of approximating the maximal inscribed ellipsoid for a polytope
• Complexity analysis of the analytic center cutting plane method that uses multiple cuts
• Shallow, deep and very deep cuts in the analytic center cutting plane method.
• Containing and shrinking ellipsoids in the path-following algorithm
• A note on some analytic center cutting plane methods for convex feasibility and minimization problems
• A new algorithm for minimizing convex functions over convex sets
• A cutting plane algorithm for convex programming that uses analytic centers
• Complexity estimates of some cutting plane methods based on the analytic barrier
• Improved Bounds and Containing Ellipsoids in Karmarkar's Linear Programming Algorithm
• Polynomial algorithms in linear programming
• Decomposition and Nondifferentiable Optimization with the Projective Algorithm
• Path-Following Methods for Linear Programming
• A Potential Reduction Algorithm Allowing Column Generation
• A Complexity Reduction for the Long-Step Path-Following Algorithm for Linear Programming
• A central cutting plane algorithm for the convex programming problem
• Analysis of a Cutting Plane Method That Uses Weighted Analytic Center and Multiple Cuts
• Complexity Analysis of an Interior Cutting Plane Method for Convex Feasibility Problems

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