Newton-Type Optimal Thresholding Algorithms for Sparse Optimization Problems

Optimal Newton-type methods for nonconvex smooth optimization problems

We consider a general class of second-order iterations for unconstrained optimization that includes regularization and trust-region variants of Newton’s method. For each method in this class, we exhibit a smooth, bounded-below objective function, whose gradient is globally Lipschitz continuous within an open convex set containing any iterates encountered and whose Hessian is α−Hölder continuous...

Newton-type algorithms for robot motion optimization

This paper presents a class of Newton-type algori thms fo r the optimization of robot motions that take in to account the dynamics. Using techniques f rom the theory of L ie groups and Lie algebras, the equations of mot ion of a rigid multibody sys tem can be formulated in such a way that both the f irst and second derivatives of the dynamic equations with respect t o arbitrary jo in t variable...

Al . : Newton - Type Algorithms for Robot Motion Optimization 3

Newton-Type Methods for Optimization Problems without Constraint Qualifications

We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular-value decomposition, we derive a modified primal-dual optimality system whose solution is locally unique, n...

Parallel Local Elimination Algorithms for Sparse Discrete Optimization Problems

The development and study of a parallel implementation of the graph-based local elimination algorithms on novel emergent parallel GPU-based architectures for solving sparse discrete optimization (DO) problems are discussed.