In this paper we present new iterative algorithms in convex metric spaces. We show that these iterative schemes are convergent to the fixed point of a single-valued contraction operator. Then we make the comparison of their rate of convergence. Additionally, numerical examples for these iteration processes are given.

In low dimensions, the relatively easily implementable acceptance-rejection method for generating polyhedral convex contoured uniform distributions is compared to more sophisticated particular methods from the literature, and applied to drug combination studies. Based upon a stochastic representation, the method is extended to the general class of polyhedral convex contoured distributions of kn...

In this work we present a quantum algorithm for multiobjective combinatorial optimization. We show that the adiabatic algorithm of Farhi et al. [arXiv:quant-ph/0001106] can be used by mapping a multiobjective combinatorial optimization problem onto a Hamiltonian using a convex combination among objectives. We present mathematical properties of the eigenspectrum of the associated Hamiltonian and...

Abstract: Trivariate barycentric coordinates can be used both to express a point inside a tetrahedron as a convex combination of the four vertices and to linearly interpolate data given at the vertices. In this paper we generalize these coordinates to convex polyhedra and the kernels of star-shaped polyhedra. These coordinates generalize in a natural way a recently constructed set of coordinate...

Knowing the fact that the main weakness of the most standard methods including k-means and hierarchical data clustering is their sensitivity to initialization and trapping to local minima, this paper proposes a modification of convex data clustering  in which there is no need to  be peculiar about how to select initial values. Due to properly converting the task of optimization to an equivalent...

We consider the problem of aggregating menus. Each agent submits a menu of options, which the social rule aggregates into a single menu. First, we study a general environment where menus are arbitrary subsets, and characterize a union rule which takes the union of individual menus. Second, we study a probabilistic environment where menus are closed convex subsets of lotteries over options, and ...

This research aims to present a linear operator Lp,q?,?,?f utilizing the q-Mittag–Leffler function. Then, we introduce subclass of harmonic (p,q)-convex functions HTp,q(?,W,V) related Janowski For p-valent f class, investigate geometric properties, such as coefficient estimates, convex combination, extreme points, and Hadamard product. Finally, closure property is derived using under q-Bernardi...

The probability of error of classification methods based on convex combinations of simple base classifiers by “boosting” algorithms is investigated. We show in this talk that certain regularized boosting algorithms provide Bayes-risk consistent classifiers under the only assumption that the Bayes classifier may be approximated by a convex combination of the base classifiers. Non-asymptotic dist...

Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of themappings. Next, using this operator, we construct an iterative sequence to approximate common fixed point...