A new framework for analyzing Fejer convergent algorithms is presented. Using this framework we define a very general class of Fejer convergent algorithms and establish its convergence properties. We also introduce a new definition of approximations of resolvents which preserve some useful features of the exact resolvent, and use this concept to present an unifying … Read more
We study the exploitation of a one species forest plantation when timber price is uncertain. The work focuses on providing optimality conditions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We use risk averse stochastic dynamic programming and use the Conditional Value-at-Risk (CVaR) as our … Read more
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements. … Read more
In this paper we consider a cardinality-constrained quadratic program that minimizes a convex quadratic function subject to a cardinality constraint and linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality … Read more
Analytical formulas are established for calculating the maximal and minimal ranks of the matrix-valued function $A + BXC$ when the rank of $X$ is fixed. Some consequences are also given. ArticleDownload View PDF
When binary linear error-correcting codes are used over symmetric channels, a relaxed version of the maximum likelihood decoding problem can be stated as a linear program (LP). This LP decoder can be used to decode at bit-error-rates comparable to state-of-the-art belief propagation (BP) decoders, but with significantly stronger theoretical guarantees. However, LP decoding when implemented … Read more
The sub-Nyquist estimation of line spectra is a classical problem in signal processing, but currently popular subspace-based techniques have few guarantees in the presence of noise and rely on a priori knowledge about system model order. Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation … Read more
The problem of packing ellipsoids of different sizes and shapes into an ellipsoidal container so as to minimize a measure of overlap between ellipsoids is considered. A bilevel optimization formulation is given, together with an algorithm for the general case and a simpler algorithm for the special case in which all ellipsoids are in fact … Read more
Scarf’s min-max order formula for the distribution-free risk-neutral newsvendor problem is a classical result in the field of inventory management. The min-max order formula provides, in closed-form, the order quantity that maximizes the worst-case expected profit associated with the demand of a single product when only the mean and variance of the product’s demand distribution, … Read more
Recently there has been intensive interest on approximation of the NP-hard submodular maximization problem due to their theoretical and practical significance. In this work, we extend this line of research by focusing on the simultaneous approximation of multiple submodular function maximization. We address existence and nonexistence results for both deterministic and randomized approximation when the … Read more