We study piecewise decomposition methods for mathematical programs with equilibrium constraints (MPECs) for which all constraint functions are linear. At each iteration of a decomposition method, one step of a nonlinear programming scheme is applied to one piece of the MPEC to obtain the next iterate. Our goal is to understand global convergence to B-stationary points of these methods when the ...

This paper is concerned with the ill-posed problem of identifying a parameter in an elliptic equation. Its solution is obtained by applying trust region method, which exhibits attractive theoretical convergence properites and seems promising. Numerical experiment is given to illustrate the eeciency of the proposed method.

Legible motion — motion that communicates its intent to a human observer — is crucial for enabling seamless human-robot collaboration. In this paper, we propose a functional gradient optimization technique for autonomously generating legible motion. Our algorithm optimizes a legibility metric inspired by the psychology of action interpretation in humans, resulting in motion trajectories that pu...

In this article, we propose a method for solving the trust-region subproblem when a limited-memory symmetric rank-one matrix is used in place of the true Hessian matrix. The method takes advantage of two shape-changing norms to decompose the trust-region subproblem into two separate problems, one of which has a closed-form solution and the other one is easy to solve. Sufficient conditions for g...

Limited memory quasi-Newton methods and trust-region methods represent two efficient approaches used for solving unconstrained optimization problems. A straightforward combination of them deteriorates the efficiency of the former approach, especially in the case of large-scale problems. For this reason, the limited memory methods are usually combined with a line search. We show how to efficient...