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A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...
Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the optimization problem and RO can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods.
In computer science and operations research, randomized rounding [1] is a widely used approach for designing and analyzing approximation algorithms. [2] [3]Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality).
Seidel (1991) gave an algorithm for low-dimensional linear programming that may be adapted to the LP-type problem framework. Seidel's algorithm takes as input the set S and a separate set X (initially empty) of elements known to belong to the optimal basis. It then considers the remaining elements one-by-one in a random order, performing ...
Las Vegas algorithms were introduced by László Babai in 1979, in the context of the graph isomorphism problem, as a dual to Monte Carlo algorithms. [3] Babai [4] introduced the term "Las Vegas algorithm" alongside an example involving coin flips: the algorithm depends on a series of independent coin flips, and there is a small chance of failure (no result).
In contrast, some authors have argued that randomization can only improve a deterministic algorithm if the deterministic algorithm was poorly designed in the first place. [21] Fred W. Glover [22] argues that reliance on random elements may prevent the development of more intelligent and better deterministic components. The way in which results ...
Randomized (Block) Coordinate Descent Method is an optimization algorithm popularized by Nesterov (2010) and Richtárik and Takáč (2011). The first analysis of this method, when applied to the problem of minimizing a smooth convex function , was performed by Nesterov (2010). [ 1 ]
The algorithm described herein is a type of local random search, where every iteration is dependent on the prior iteration's candidate solution. There are alternative random search methods that sample from the entirety of the search space (for example pure random search or uniform global random search), but these are not described in this article.