SIAM Journal on Numerical Analysis
First and second order analysis of nonlinear semidefinite programs
Mathematical Programming: Series A and B
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Robust Control via Sequential Semidefinite Programming
SIAM Journal on Control and Optimization
SIAM Journal on Optimization
Penalty/Barrier Multiplier Methods for Convex Programming Problems
SIAM Journal on Optimization
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Partially Augmented Lagrangian Method for Matrix Inequality Constraints
SIAM Journal on Optimization
Numerical Comparison of Augmented Lagrangian Algorithms for Nonconvex Problems
Computational Optimization and Applications
Spectral bundle methods for non-convex maximum eigenvalue functions: first-order methods
Mathematical Programming: Series A and B
Spectral bundle methods for non-convex maximum eigenvalue functions: second-order methods
Mathematical Programming: Series A and B
Controller Design via Nonsmooth Multidirectional Search
SIAM Journal on Control and Optimization
On the solution of large-scale SDP problems by the modified barrier method using iterative solvers
Mathematical Programming: Series A and B
Brief paper: Nonsmooth optimization for multiband frequency domain control design
Automatica (Journal of IFAC)
Generalized Hadamard Product and the Derivatives of Spectral Functions
SIAM Journal on Matrix Analysis and Applications
On the convergence of augmented Lagrangian methods for nonlinear semidefinite programming
Journal of Global Optimization
A homotopy method for nonlinear semidefinite programming
Computational Optimization and Applications
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We consider nonlinear optimization programs with matrix inequality constraints, also known as nonlinear semidefinite programs. We prove local convergence for an augmented Lagrangian method which uses smooth spectral penalty functions. The sufficient second-order no-gap optimality condition and a suitable implicit function theorem are used to prove local linear convergence without the need to drive the penalty parameter to 0.