We combine a sequence of contractive mappings {fn} and propose a generalized viscosity approximation method. One side, we consider a nonexpansive mapping S with the nonempty fixed point set defined on a nonempty closed convex subset C of a real Hilbert space H and design a new iterative method to approximate some fixed point of S, which is also a unique solution of the variational inequality. O...

Kernel Approximation Methods for Speech Recognition

The main objective of this paper is to analyze the evolution strategy by use of stochastic approximation methods Both constant and decreasing step size algorithms are studied Convergence and estimation error bounds for the evolution strategy are developed First the algorithm is converted to a recursively de ned scheme of stochastic approximation type Then the analysis is carried out by using th...

Modern statistical models are often intractable, and approximation methods can be required to perform inference on them. Many different methods can be employed in most contexts, but not all are fully understood. The current thesis is an investigation into the use of various approximation methods for performing inference on latent variable models. Composite likelihoods are used as surrogates for...

High-dimensional representations, such as radial basis function networks or tile coding, are common choices for policy evaluation in reinforcement learning. Learning with such high-dimensional representations, however, can be expensive, particularly for matrix methods, such as least-squares temporal difference learning or quasi-Newton methods that approximate matrix step-sizes. In this work, we...

Mortar method is proposed to form a macroscopic model for a problem with a multiscale conductivity. The macroscopic model is built on the coarse uniform grid quipped for the problem domain. For each uniform grid, artificial neighboring cells are attached to form a model which includes the localized microscale model. For the proposed model, a very fine mesh is introduced to resolve the microscal...

Positive semidefinite Toeplitz matrix constraints arise naturally in a variety of problems in engineering. This paper deals with the numerical of this problem. Our approach is based on (i) interior point primal-dual path-following method; (ii) a projection algorithm which converges globally but slowly; (iii) the filterSQP method which is faster. Hybrid methods that attempt to combine the best f...

In this paper we consider sparse approximation problems, that is, general l0 minimization problems with the l0-“norm” of a vector being a part of constraints or objective function. In particular, we first study the first-order optimality conditions for these problems. We then propose penalty decomposition (PD) methods for solving them in which a sequence of penalty subproblems are solved by a b...

Kernelization algorithms in the context of Parameterized Complexity are often based on a combination of reduction rules and combinatorial insights. We will expose in this paper a similar strategy for obtaining polynomial-time approximation algorithms. Our method features the use of approximation-preserving reductions, akin to the notion of parameterized reductions. We exemplify this method to o...

Complex polynomial optimization problems arise from real-life applications including radar code design, MIMO beamforming, and quantum mechanics. In this paper, we study complex polynomial optimization models whereby the objective function takes one of the following three forms: (1) multilinear; (2) homogeneous polynomial; (3) a conjugate symmetric form. On the constraint side, the decision vari...