In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions. However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it...

A generalization of the steepest descent and other methods for solving a large scale symmetric positive definitive system Ax = b is presented. Given a positive integer m, the new iteration is given by xk+1 = xk −λ(xν(k))(Axk − b), where λ(xν(k)) is the steepest descent step at a previous iteration ν(k) ∈ {k, k−1, . . . , max{0, k−m}}. The global convergence to the solution of the problem is est...

Multivariate spectral gradient method is proposed for solving unconstrained optimization problems. Combined with some quasi-Newton property multivariate spectral gradient method allows an individual adaptive stepsize along each coordinate direction, which guarantees that the method is finitely convergent for positive definite quadratics. Especially, it converges no more than two steps for posit...

We consider multigrid cycles based on the recursive use of a two–grid method, in which the coarse–grid system is solved by μ ≥ 1 steps of a Krylov subspace iterative method. The approach is further extended by allowing such inner iterations only at levels of given multiplicity, a V–cycle formulation being used at all other levels. For symmetric positive definite systems and symmetric multigrid ...

In this paper, we introduce the truncated primal-infeasible dual-feasible interior point algorithm for linear programming and describe an implementation of this algorithm for solving the minimum cost network flow problem. In each iteration, the linear system that determines the search direction is computed inexactly, and the norm of the resulting residual vector is used in the stopping criteria...

The (micro-)finite element analysis based on three-dimensional computed tomography (CT) data of human bone takes place on complicated domains composed of often hundreds of millions of voxel elements. The finite element analysis is used to determine stresses and strains at the trabecular level of bone. It is even used to predict fracture of osteoporotic bone. However, the computed stresses can d...

In this paper, we propose an alternating proximal gradient method that solves convex minimization problems with three or more separable blocks in the objective function. Our method is based on the framework of alternating direction method of multipliers. The main computational effort in each iteration of the proposed method is to compute the proximal mappings of the involved convex functions. T...

In this paper we present a fast iterative image superresolution algorithm using preconditioned conjugate gradient method. To avoid explicitly computing the tolerance in the inverse filter based preconditioner scheme, a new Wiener filter based preconditioner for the conjugate gradient method is proposed to speed up the convergence. The circulant-block structure of the preconditioner allows effic...

In this work, we propose an inexact projected gradient-like method for solving smooth constrained vector optimization problems. In the unconstrained case, we retrieve the steepest descent method introduced by Graña Drummond and Svaiter. In the constrained setting, the method we present extends the exact one proposed by Graña Drummond and Iusem, since it admits relative errors on the search dire...

In the pursuit of increasingly intelligent learning systems, abstraction plays a vital role in enabling sophisticated decisions to be made in complex environments. The options framework provides formalism for such abstraction over sequences of decisions. However most models require that options be given a priori, presumably specified by hand, which is neither efficient, nor scalable. Indeed, it...