Functions and Sets of Smooth Substructure: Relationships and Examples
Computational Optimization and Applications
An inequality constrained nonlinear Kalman-Bucy smoother by interior point likelihood maximization
Automatica (Journal of IFAC)
A proximal method for identifying active manifolds
Computational Optimization and Applications
An approximate decomposition algorithm for convex minimization
Journal of Computational and Applied Mathematics
Generic Optimality Conditions for Semialgebraic Convex Programs
Mathematics of Operations Research
Accelerated Block-coordinate Relaxation for Regularized Optimization
SIAM Journal on Optimization
Manifold identification in dual averaging for regularized stochastic online learning
The Journal of Machine Learning Research
| Hi-index | 0.01 |
Nonsmoothness pervades optimization, but the way it typically arises is highly structured. Nonsmooth behavior of an objective function is usually associated, locally, with an active manifold: on this manifold the function is smooth, whereas in normal directions it is "vee-shaped." Active set ideas in optimization depend heavily on this structure. Important examples of such functions include the pointwise maximum of some smooth functions and the maximum eigenvalue of a parametrized symmetric matrix. Among possible foundations for practical nonsmooth optimization, this broad class of "partly smooth" functions seems a promising candidate, enjoying a powerful calculus and sensitivity theory. In particular, we show under a natural regularity condition that critical points of partly smooth functions are stable: small perturbations to the function cause small movements of the critical point on the active manifold.