Sparse optimization refers to an optimization problem involving the zero-norm in objective or constraints. In this paper, nonconvex approximation approaches for sparse optimization have been studied with a unifying point of view in DC (Difference of Convex functions) programming framework. Considering a common DC approximation of the zero-norm including all standard sparse inducing penalty func...

We study sparse approximate solutions to convex optimization problems. It is known that in many engineering applications researchers are interested in an approximate solution of an optimization problem as a linear combination of elements from a given system of elements. There is an increasing interest in building such sparse approximate solutions using different greedy-type algorithms. The prob...

Sparse signal recovery from a small number of random measurements is a well known NP-hard to solve combinatorial optimization problem, with important applications in signal and image processing. The standard approach to the sparse signal recovery problem is based on the basis pursuit method. This approach requires the solution of a large convex optimization problem, and therefore suffers from h...

Bayesian optimization schemes often rely on Gaussian processes (GP). GP models are very flexible, but are known to scale poorly with the number of training points. While several efficient sparse GP models are known, they have limitations when applied in optimization settings. We propose a novel Bayesian optimization framework that uses sparse online Gaussian processes. We introduce a new updati...

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of a sum of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to get a simpler representation of a “sparse” polynomial as a sum of squares of sparse pol...

We proposed several strategies to improve the sparse optimization methods for solving Sudoku puzzles. Further, we defined a new difficult level for Sudoku. We tested our proposed methods on Sudoku puzzles data-set. Numerical results showed that we can improve the accurate recovery rate from 84%+ to 99%+ by the L1 sparse optimization method.

Representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and SDP (semidefinite programming) relaxation of polynomial optimization problems. We disscuss effective methods to obtain a simpler representation of a “sparse” polynomial as a sum of squares of sparse p...