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
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 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
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 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