We address the problem of preconditioning a sequence of saddle point linear systems arising in the solution of PDE-constrained optimal control problems via active-set Newton methods, with control and (regularized) state constraints. We present two new preconditioners based on a full block matrix factorization of the Schur complement of the Jacobian matrices, where the active-set … Read more
The MVE estimator is an important tool in robust regression and outlier detection in statistics. We develop fast and efficient algorithms for the MVE estimator problem and discuss how they can be implemented efficiently. The novelty of our approach stems from the recent developments in the first-order algorithms for solving the related Minimum Volume Enclosing … Read more
This paper studies a statistical problem called instrumental variable quantile regres- sion (IVQR). We model IVQR as a convex quadratic program with complementarity constraints and—although this type of program is generally NP-hard—we develop a branch-and-bound algorithm to solve it globally. We also derive bounds on key vari- ables in the problem, which are valid asymptotically … Read more
The dimer method is a Hessian-free algorithm for computing saddle points. We augment the method with a linesearch mechanism for automatic step size selection as well as preconditioning capabilities. We prove local linear convergence. A series of numerical tests demonstrate significant performance gains. Citationhttp://arxiv.org/abs/1407.2817ArticleDownload View PDF
In model-based design of cyber-physical systems, such as switched mixed-signal circuits or software-controlled physical systems, it is common to develop a sequence of system models of different fidelity and complexity, each appropriate for a particular design or verification task. In such a sequence, one model is often derived from the other by a process of … Read more
We consider an extension of a noncooperative game where players have joint binding constraints. In this model, the constrained equilibrium can not be implemented within the same noncooperative framework and requires some other additional regulation procedures. We consider several approaches to resolution of this problem. In particular, a share allocation method is presented and substantiated. … Read more
In this paper, we develop a stochastic model for topology optimization. We find robust structures that minimize the compliance for a given main load having a stochastic behavior. We propose a model that takes into account the expected value of the compliance and its variance. We show that, similarly to the case of truss structures, … Read more
Infinite-dimensional linear conic formulations are described for nonlinear optimal control problems. The primal linear problem consists of finding occupation measures supported on optimal relaxed controlled trajectories, whereas the dual linear problem consists of finding the largest lower bound on the value function of the optimal control problem. Various approximation results relating the original optimal control … Read more
We consider the problem of minimizing the sum of two convex functions: one is smooth and given by a gradient oracle, and the other is separable over blocks of coordinates and has a simple known structure over each block. We develop an accelerated randomized proximal coordinate gradient (APCG) method for minimizing such convex composite functions. … Read more
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an iterative algorithm for identifying a linear subspace of $\R^n$ from data consisting of partial observations of random vectors from that subspace. This paper examines local convergence properties of GROUSE, under assumptions on the randomness of the observed vectors, the randomness of the subset of elements observed at … Read more