Related papers: An optimal convergent Collatz algorithm
In this paper, we establish the $R$-linear rate of convergence of a golden ratio algorithm for solving an equilibrium problem in a Hilbert space. Several experiments are performed to show the numerical behavior of the algorithm and also to…
The Condorcet Jury Theorem or the Miracle of Aggregation are frequently invoked to ensure the competence of some aggregate decision-making processes. In this article we explore an estimation of the prior probability of the thesis predicted…
Algorithmic collusion is an emerging concept in current artificial intelligence age. Whether algorithmic collusion is a creditable threat remains as an argument. In this paper, we propose an algorithm which can extort its human rival to…
On the set of positive integers, we consider the iterative process that maps $n$ to either $\frac{3n+1}{2}$ or $\frac{n}{2}$ depending on the parity of $n$. The Collatz conjecture states that all such sequences eventually enter the trivial…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
We intend to contribute to the Collatz dynamics problem by seeking to analyze the Collatz conjecture from the tree of numbers sequences. First, we show numerically that the distribution of odd numbers has an initial transient, and proceeds…
The theory of fuzzy mathematics has been proven very effective for defining and solving optimization problems. Fuzzy quadratic programming (FQP) is a consequence of this approach. In this paper, an algorithm has been proposed to solve FQP…
In this paper, we obtain bounds on the probability of convergence to the optimal solution for the compact Genetic Algorithm (cGA) and the Population Based Incremental Learning (PBIL). We also give a sufficient condition for convergence of…
We present convergence theory for corrected quadrature rules on uniform Cartesian grids for functions with a point singularity. We begin by deriving an error estimate for the punctured trapezoidal rule, and then derive error expansions. We…
In this paper we study the computational feasibility of an algorithm to prove orbifold equivalence between potentials describing Landau-Ginzburg models. Through a comparison with leading results of Groebner basis computations in cryptology,…
The Kaczmarz method for solving linear systems of equations is an iterative algorithm that has found many applications ranging from computer tomography to digital signal processing. Despite the popularity of this method, useful theoretical…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the…
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems…
This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…
Quantum computing takes fully advantage of the superposition principle to increase greatly (even exponentially) the speed of calculations, relative to the classical approach. The Deutsch-Jozsa algorithm is the simplest quantum algorithm…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
Prediction-correction algorithms are a highly effective class of methods for solving pseudo-convex optimization problems. The descent direction of these algorithms can be viewed as an adjustment to the gradient direction based on the…
The convergence theory for the gradient sampling algorithm is extended to directionally Lipschitz functions. Although directionally Lipschitz functions are not necessarily locally Lipschitz, they are almost everywhere differentiable and…