This paper develops Jellyfish, an algorithm for solving data-processing problems with matrix-valued decision variables regularized to have low rank. Particular examples of problems solvable by Jellyfish include matrix completion problems and least-squares problems regularized by the nuclear norm or the max-norm. Jellyfish implements a projected incremental gradient method with a biased, random ordering of the … Read more
Given a family of real or complex monic polynomials of fixed degree with one affine constraint on their coefficients, consider the problem of minimizing the root radius (largest modulus of the roots) or root abscissa (largest real part of the roots). We give constructive methods for efficiently computing the globally optimal value as well as … Read more
This paper proposes efficient algorithms for group sparse optimization with mixed L21-regularization, which arises from the reconstruction of group sparse signals in compressive sensing, and the group Lasso problem in statistics and machine learning. It is known that encoding the group information in addition to sparsity will lead to better signal recovery/feature selection. The L21-regularization … Read more
The electrical vehicle energy management can be expressed as a Bang-Bang optimal control problem. In this work, we discuss on a new formulation and about the way to approximate this optimal control problem of Bang-Bang type via a discretization technique associated with a Branch-and-Bound algorithm. The problem that we focus on, is the minimization of … Read more
The electrical vehicle energy management can be expressed as a Bang-Bang optimal control problem. In this work, we discuss on a new formulation and about the way to approximate this optimal control problem of Bang-Bang type via a discretization technique associated with a Branch-and-Bound algorithm. The problem that we focus on, is the minimization of … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Gaussian processes are the cornerstone of statistical analysis in many application ar- eas. Nevertheless, most of the applications are limited by their need to use the Cholesky factorization in the computation of the likelihood. In this work, we present a matrix-free approach for comput- ing the solution of the maximum likelihood problem involving Gaussian processes. … Read more
Surrogate models and heuristics are frequently used in the optimization engineering community as convenient approaches to deal with functions for which evaluations are expensive or noisy, or lack convexity. These methodologies do not typically guarantee any type of convergence under reasonable assumptions and frequently render slow convergence. In this paper we will show how to … Read more
Surrogate models and heuristics are frequently used in the optimization engineering community as convenient approaches to deal with functions for which evaluations are expensive or noisy, or lack convexity. These methodologies do not typically guarantee any type of convergence under reasonable assumptions and frequently render slow convergence. In this paper we will show how to … Read more