Row by row methods for semidefinite programming

We present a row-by-row (RBR) method for solving semidefinite programming (SDP) problem based on solving a sequence of problems obtained by restricting the n-dimensional positive semidefinite constraint on the matrix X. By fixing any (n-1)-dimensional principal submatrix of X and using its (generalized) Schur complement, the positive semidefinite constraint is reduced to a simple second-order … Read more

Continuous GRASP with a local active-set method for bound-constrained global optimization

Global optimization seeks a minimum or maximum of a multimodal function over a discrete or continuous domain. In this paper, we propose a hybrid heuristic – based on the CGRASP and GENCAN methods – for finding approximate solutions for continuous global optimization problems subject to box constraints. Experimental results illustrate the relative effectiveness of CGRASP-GENCAN … Read more

Convergence Rate of Stochastic Gradient Search in the Case of Multiple and Non-Isolated Minima

The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are derived. As opposed to the existing results, the results presented in this paper allow the objective function to have multiple, non-isolated minima, … Read more

NESTA: A Fast and Accurate First-order Method for Sparse Recovery

Accurate signal recovery or image reconstruction from indirect and possibly under- sampled data is a topic of considerable interest; for example, the literature in the recent field of compressed sensing is already quite immense. Inspired by recent breakthroughs in the development of novel fi rst-order methods in convex optimization, most notably Nesterov’s smoothing technique, this paper … Read more

Compressed Sensing with Quantized Measurements

We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an l1 regularization term. Using a first order method developed … Read more

An Improved Algorithm for the Solution of the Entire Regulation Path of Support Vector Machine

This paper describes an improved algorithm for the numerical solution to the Support Vector Machine (SVM) classification problem for all values of the regularization parameter, C. The algorithm is motivated by the work of Hastie \emph{et. al.} and follows the main idea of tracking the optimality conditions of the SVM solution for descending value of … Read more

Distributionally Robust Optimization and its Tractable Approximations

In this paper, we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust, and more flexible than the standard technique of using linear rules. Our framework begins by … Read more

Option – Alloction funds- Transaction costs

The present article studies the efficiency of a strategy, incorporating some options and seeking to super-duplicate a standard allocation policy. The replication strategy allows reducing transaction cost effects. The replication means optimizing two objective-functions: MSE (Mean-squared Errors) and WMSE (Weighted Mean-squared Errors). Tests on portfolio efficiency concern, at first time, a long-term investor with Out-The-Country … Read more

A Modified Frank-Wolfe Algorithm for Computing Minimum-Area Enclosing Ellipsoidal Cylinders: Theory and Algorithms

We study a first-order method to find the minimum cross-sectional area ellipsoidal cylinder containing a finite set of points. This problem arises in optimal design in statistics when one is interested in a subset of the parameters. We provide convex formulations of this problem and its dual, and analyze a method based on the Frank-Wolfe … Read more

Homogeneous Cone Complementarity Problems and $ Properties

We consider existence and uniqueness properties of a solution to homogeneous cone complementarity problem (HCCP). Employing the $T$-algebraic characterization of homogeneous cones, we generalize the $P, P_0, R_0$ properties for a nonlinear function associated with the standard nonlinear complementarity problem to the setting of HCCP. We prove that if a continuous function has either the … Read more