The $\U$-Lagrangian of the Maximum Eigenvalue Function

DOI10.1137/S1052623496311776zbMath0961.65059MaRDI QIDQ4702298

Oustry, François

Publication date: 24 November 1999

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

zbMATH Keywords

algorithmsnonsmooth analysisconvex optimizationeigenvalue optimizationsequential quadratic programminggeneralized derivativesecond-order derivative

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Numerical mathematical programming methods (65K05) Convex programming (90C25) Nonsmooth analysis (49J52) Linear programming (90C05) Convex functions and convex programs in convex geometry (52A41)

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The bundle scheme for solving arbitrary eigenvalue optimizations ⋮ A Second-Order Bundle Method Based on -Decomposition Strategy for a Special Class of Eigenvalue Optimizations ⋮ The spectral bundle method with second-order information ⋮ A \(\mathcal{UV}\)-method for a class of constrained minimized problems of maximum eigenvalue functions ⋮ A space decomposition scheme for maximum eigenvalue functions and its applications ⋮ Harnessing Structure in Composite Nonsmooth Minimization ⋮ The space decomposition method for the sum of nonlinear convex maximum eigenvalues and its applications ⋮ The space decomposition theory for a class of eigenvalue optimizations ⋮ The space decomposition theory for a class of semi-infinite maximum eigenvalue optimizations ⋮ \(\mathcal{UV}\)-theory of a class of semidefinite programming and its applications ⋮ A fast space-decomposition scheme for nonconvex eigenvalue optimization ⋮ Smooth convex approximation to the maximum eigenvalue function ⋮ The 𝒰-Lagrangian of a convex function ⋮ A Decomposition Algorithm for the Sums of the Largest Eigenvalues ⋮ First- and second-order epi-differentiability in eigenvalue optimization ⋮ Geometrical interpretation of the predictor-corrector type algorithms in structured optimization problems ⋮ Newton methods for nonsmooth convex minimization: connections among \(\mathcal U\)-Lagrangian, Riemannian Newton and SQP methods ⋮ Spectral bundle methods for non-convex maximum eigenvalue functions: first-order methods ⋮ Spectral bundle methods for non-convex maximum eigenvalue functions: second-order methods ⋮ On Solving the Convex Semi-Infinite Minimax Problems via Superlinear 𝒱𝒰 Incremental Bundle Technique with Partial Inexact Oracle

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