A non-interior continuation method for second-order cone programming

DOI10.1080/02331930701763421zbMath1177.90318OpenAlexW2062260849MaRDI QIDQ3648622

Xiaoni Chi, San-Yang Liu

Publication date: 27 November 2009

Published in: Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02331930701763421

zbMATH Keywords

global convergencesecond-order cone programmingnon-interior continuation methodlocal superlinear convergence

Mathematics Subject Classification ID

Numerical mathematical programming methods (65K05) Convex programming (90C25) Nonlinear programming (90C30)

Related Items

A new non-interior continuation method for solving the second-order cone complementarity problem ⋮ Smoothing functions and algorithm for nonsymmetric circular cone complementarity problems. ⋮ A smoothing Newton method for the second-order cone complementarity problem. ⋮ Improved convergence analysis of a smoothing Newton method for the circular cone programming ⋮ A smoothing Newton method for second-order cone optimization based on a new smoothing function ⋮ Smoothing Newton algorithm for the second-order cone programming with a nonmonotone line search ⋮ A non-monotone regularization Newton method for the second-order cone complementarity problem ⋮ Analysis of a non-monotone smoothing-type algorithm for the second-order cone programming. ⋮ A globally and quadratically convergent smoothing Newton method for solving second-order cone optimization ⋮ Quadratic convergence to the optimal solution of second-order conic optimization without strict complementarity ⋮ Quadratic convergence analysis of a nonmonotone Levenberg-Marquardt type method for the weighted nonlinear complementarity problem ⋮ A smoothing-type algorithm for the second-order cone complementarity problem with a new nonmonotone line search ⋮ A one-parametric class of smoothing functions and an improved regularization Newton method for the NCP ⋮ A new noninterior continuation method for solving a system of equalities and inequalities ⋮ Analysis of smoothing-type algorithms for the convex second-order cone programming

Uses Software

• SDPT3

Cites Work

• Applications of second-order cone programming
• Superlinear/quadratic one-step smoothing Newton method for \(P_0\)-NCP without strict complementarity
• Predictor-corrector smoothing Newton method, based on a new smoothing function, for solving the nonlinear complementarity problem with a \(P_0\) function
• Second-order cone programming
• Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems
• Sub-quadratic convergence of a smoothing Newton algorithm for the \(P_0\)- and monotone LCP
• Interior point methods for second-order cone programming and OR applications
• A nonsmooth version of Newton's method
• Strong semismoothness of the Fischer-Burmeister SDC and SOC complementarity functions
• Smoothing Functions for Second-Order-Cone Complementarity Problems
• Semismooth and Semiconvex Functions in Constrained Optimization
• Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
• Improving the convergence of non-interior point algorithms for nonlinear complementarity problems
• A Global Linear and Local Quadratic Noninterior Continuation Method for Nonlinear Complementarity Problems Based on Chen--Mangasarian Smoothing Functions
• A Combined Smoothing and Regularization Method for Monotone Second-Order Cone Complementarity Problems