Approximate augmented Lagrangian functions and nonlinear semidefinite programs

DOI10.1007/s10114-005-0702-6zbMath1126.90057OpenAlexW2076425042MaRDI QIDQ2505379

Xiao Qi Yang, Xue Xiang Huang, Kok Lay Teo

Publication date: 4 October 2006

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0702-6

zbMATH Keywords

convergencesemidefinite programmingdualitystationary pointaugmented Lagrangianexact penalty

Mathematics Subject Classification ID

Semidefinite programming (90C22) Nonlinear programming (90C30)

Related Items

A primal–dual penalty method via rounded weighted-ℓ₁ Lagrangian duality ⋮ Convergence to a second-order critical point by a primal-dual interior point trust-region method for nonlinear semidefinite programming ⋮ Global convergence of modified augmented Lagrangian methods for nonlinear semidefinite programming ⋮ On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming ⋮ A stabilized sequential quadratic semidefinite programming method for degenerate nonlinear semidefinite programs ⋮ On relations of vector optimization results with \(C^{1,1}\) data ⋮ An interior point method with a primal-dual quadratic barrier penalty function for nonlinear semidefinite programming ⋮ Differential equation method based on approximate augmented Lagrangian for nonlinear programming ⋮ On the approximate augmented Lagrangian for nonlinear symmetric cone programming ⋮ Primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function ⋮ Optimality conditions and global convergence for nonlinear semidefinite programming ⋮ An augmented Lagrangian algorithm for nonlinear semidefinite programming applied to the covering problem ⋮ A primal-dual interior point trust-region method for nonlinear semidefinite programming ⋮ Unnamed Item ⋮ Successive linearization methods for nonlinear semidefinite programs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An exterior point method for computing points that satisfy second-order necessary conditions for a \(C^{1,1}\) optimization problem
• First and second order analysis of nonlinear semidefinite programs
• Optimality conditions for nonconvex semidefinite programming
• Interior-point algorithms for semidefinite programming based on a nonlinear formulation
• Solving a class of semidefinite programs via nonlinear programming
• An interior method for nonconvex semidefinite programs
• A Nonlinear Lagrangian Approach to Constrained Optimization Problems
• Lagrange Multipliers and Optimality
• Semidefinite optimization
• Penalty methods for computing points that satisfy second order necessary conditions
• Variational Analysis
• Penalty/Barrier multiplier algorthm for semidefinit programming^∗
• Robust Control via Sequential Semidefinite Programming
• Second Order Optimality Conditions Based on Parabolic Second Order Tangent Sets
• Advances in Linear Matrix Inequality Methods in Control
• Semidefinite Programs: New Search Directions, Smoothing-Type Methods, and Numerical Results
• Second Derivatives for Optimizing Eigenvalues of Symmetric Matrices
• Semidefinite Programming
• Penalty and Barrier Methods: A Unified Framework
• Handbook of semidefinite programming. Theory, algorithms, and applications
• Optimal design of trusses under a nonconvex global buckling constraint

This page was built for publication: Approximate augmented Lagrangian functions and nonlinear semidefinite programs