In many machine learning problems such as the dual form of SVM, the objective function to be minimized is convex but not strongly convex. This fact causes difficulties in obtaining the complexity of some commonly used optimization algorithms. In this paper, we proved the global linear convergence on a wide range of algorithms when they are applied to some non-strongly convex problems. In partic...

We consider Acyclic Unique Sink Orientations of the n-dimensional hyper-cube (AUSOs), that is, acyclic orientations of the edges of the hyper-cube such that any sub-cube has a unique vertex of maximal in-degree. We study the Policy Iteration (PI) algorithm, also known as Bottom-Antipodal or Switch-All, to nd the global sink: starting from an initial vertex π0, i = 0, the outgoing links at the p...

We consider a broad class of first-order optimization algorithms which are oblivious, in the sense that their step sizes are scheduled regardless of the function under consideration, except for limited side-information such as smoothness or strong convexity parameters. With the knowledge of these two parameters, we show that any such algorithm attains an iteration complexity lower bound of Ω( √...

Solving Markov Decision Processes (MDPs) is a recurrent task in engineering. Even though it is known that solutions for minimizing the infinite horizon expected reward can be found in polynomial time using Linear Programming techniques, iterative methods like the Policy Iteration algorithm (PI) remain usually the most efficient in practice. This method is guaranteed to converge in a finite numb...

in this paper, we represent an inexact inverse subspace iteration method for com- puting a few eigenpairs of the generalized eigenvalue problem ax = bx[q. ye and p. zhang, inexact inverse subspace iteration for generalized eigenvalue problems, linear algebra and its application, 434 (2011) 1697-1715 ]. in particular, the linear convergence property of the inverse subspace iteration is preserved.

Big Data problems in Machine Learning have large number of data points or large number of features, or both, which make training of models difficult because of high computational complexities of single iteration of learning algorithms. To solve such learning problems, Stochastic Approximation offers an optimization approach to make complexity of each iteration independent of number of data poin...

The accelerated proximal gradient (APG) method, first proposed by Nesterov for minimizing smooth convex functions, later extended by Beck and Teboulle to composite convex objective functions, and studied in a unifying manner by Tseng, has proven to be highly efficient in solving some classes of large scale structured convex optimization (possibly nonsmooth) problems, including nuclear norm mini...

We propose a first order interior point algorithm for a class of nonLipschitz and nonconvex minimization problems with box constraints, which arise from applications in variable selection and regularized optimization. The objective functions of these problems are continuously differentiable typically at interior points of the feasible set. Our first order algorithm is easy to implement and the ...

We propose empirical dynamic programming algorithms for Markov decision processes (MDPs). In these algorithms, the exact expectation in the Bellman operator in classical value iteration is replaced by an empirical estimate to get ‘empirical value iteration’ (EVI). Policy evaluation and policy improvement in classical policy iteration are also replaced by simulation to get ‘empirical policy iter...

Most of the localization algorithms have performed localization utilizing absolute point-topoint distance estimates. If the sensor network is not cooperative, there’s no information about the strength of the original signal so that the location of a target node is hard to be found. It allows ratiometric location algorithm to be proposed. GPS algorithm give accurate location of unknown node, how...