The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. in signal/image processing and statistics. A standard tool for dealing with sparse recovery is the ℓ1-regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version … Read more
In this paper we consider a network with P nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector x* minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function … Read more
We present improvements to branch and bound techniques for globally optimizing functions with Lipschitz continuity properties by developing novel bounding procedures and parallelisation strategies. The bounding procedures involve nonconvex quadratic or cubic lower bounds on the objective and use estimates of the spectrum of the Hessian or derivative tensor, respectively. As the nonconvex lower bounds … Read more
This work reports on modeling and numerical experience in solving the long-term design and operation planning problem of the Brazilian natural gas network. A stochastic approach to address uncertainties related to the gas demand is considered. Representing uncertainties by finitely many scenarios increases the size of the resulting optimization problem, and therefore the difficulty to … Read more
We consider the problem of scheduling on uniform processors with nonsimultaneous machine available times with the purpose of mini\-mi\-zing the maximum completion time. We give a variant of the Multifit algorithm which generates schedules which end within $1.382$ times the optimal maximum completion times. This results from properties of the Multifit algorithm when used for … Read more
The well-known symmetric rank-one trust-region method—where the Hessian approximation is generated by the symmetric rank-one update—is generalized to the problem of minimizing a real-valued function over a $d$-dimensional Riemannian manifold. The generalization relies on basic differential-geometric concepts, such as tangent spaces, Riemannian metrics, and the Riemannian gradient, as well as on the more recent notions … Read more
We deal with monotone inclusion problems of the form $0\in Ax+Dx+N_C(x)$ in real Hilbert spaces, where $A$ is a maximally monotone operator, $D$ a cocoercive operator and $C$ the nonempty set of zeros of another cocoercive operator. We propose a forward-backward penalty algorithm for solving this problem which extends the one proposed by H. Attouch, … Read more
We address the conjecture proposed by Gabor Pataki that every facially exposed cone is nice. We show that the conjecture is true in the three-dimensional case, however, there exists a four-dimensional counterexample of a cone that is facially exposed but is not nice. CitationCRN, University of BallaratArticleDownload View PDF
Nonmonotone line search methods for unconstrained minimization with the objective functions in the form of mathematical expectation are considered. The objective function is approximated by the sample average approximation (SAA) with a large sample of fixed size. The nonmonotone line search framework is embedded with a variable sample size strategy such that different sample size … Read more
The uniqueness of sparsest solutions of underdetermined linear systems plays a fundamental role in the newly developed compressed sensing theory. Several new algebraic concepts, including the sub-mutual coherence, scaled mutual coherence, coherence rank, and sub-coherence rank, are introduced in this paper in order to develop new and improved sufficient conditions for the uniqueness of sparsest … Read more