[BOOK][B] Variational analysis and applications

BS Mordukhovich - 2018 - Springer
Boris S. Mordukhovich Page 1 Springer Monographs in Mathematics Boris S. Mordukhovich
Variational Analysis and Applications Page 2 Springer Monographs in Mathematics Editors-in-Chief …

A Newton-CG augmented Lagrangian method for semidefinite programming

XY Zhao, D Sun, KC Toh - SIAM Journal on Optimization, 2010 - SIAM
We consider a Newton-CG augmented Lagrangian method for solving semidefinite
programming (SDP) problems from the perspective of approximate semismooth Newton …

Combining convex–concave decompositions and linearization approaches for solving BMIs, with application to static output feedback

QT Dinh, S Gumussoy, W Michiels… - IEEE Transactions on …, 2011 - ieeexplore.ieee.org
A novel optimization method is proposed to minimize a convex function subject to bilinear
matrix inequality (BMI) constraints. The key idea is to decompose the bilinear map** as a …

Linear rate convergence of the alternating direction method of multipliers for convex composite programming

D Han, D Sun, L Zhang - Mathematics of Operations …, 2018 - pubsonline.informs.org
In this paper, we aim to prove the linear rate convergence of the alternating direction method
of multipliers (ADMM) for solving linearly constrained convex composite optimization …

A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions

X Li, D Sun, KC Toh - Mathematical Programming, 2016 - Springer
This paper is devoted to the design of an efficient and convergent semi-proximal alternating
direction method of multipliers (ADMM) for finding a solution of low to medium accuracy to …

An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems

Y Zhang, N Zhang, D Sun, KC Toh - Mathematical Programming, 2020 - Springer
The sparse group Lasso is a widely used statistical model which encourages the sparsity
both on a group and within the group level. In this paper, we develop an efficient augmented …

Differentiating nonsmooth solutions to parametric monotone inclusion problems

J Bolte, E Pauwels, A Silveti-Falls - SIAM Journal on Optimization, 2024 - SIAM
We leverage path differentiability and a recent result on nonsmooth implicit differentiation
calculus to give sufficient conditions ensuring that the solution to a monotone inclusion …

The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming

D Sun, J Sun, L Zhang - Mathematical Programming, 2008 - Springer
We analyze the rate of local convergence of the augmented Lagrangian method in nonlinear
semidefinite optimization. The presence of the positive semidefinite cone constraint requires …

A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block

M Li, D Sun, KC Toh - Asia-Pacific Journal of Operational Research, 2015 - World Scientific
In this paper, we present a semi-proximal alternating direction method of multipliers
(sPADMM) for solving 3-block separable convex minimization problems with the second …

On efficiently solving the subproblems of a level-set method for fused lasso problems

X Li, D Sun, KC Toh - SIAM Journal on Optimization, 2018 - SIAM
In applying the level-set method developed in [E. Van den Berg and MP Friedlander, SIAM J.
Sci. Comput., 31 (2008), pp. 890--912] and [E. Van den Berg and MP Friedlander, SIAM J …