Shortest Path: Properties of the Algorithm

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Explores critical phenomena in complex systems, including stochastic objects, percolation, and combinatorial optimization.

Descent methods and line search: Finiteness of the line search algorithm

Explores the Wolfe conditions for line search algorithms and proves the finiteness of the line search parameter.

Distributed Intelligent Systems: Self-Organization and Foraging Strategies

Explores self-organization in natural systems and foraging strategies of ants, including the Traveling Salesman Problem and Ant Colony Optimization algorithms.

Choosing a Step Size

Explores choosing a step size in optimization on manifolds, including backtracking line-search and the Armijo method.

Minimum Spanning Trees

Covers the implementation and analysis of disjoint sets data structure and introduces the concept of minimum spanning trees.

Simplex Algorithm

Covers the Simplex algorithm for function minimization with linear constraints.

Markov Chains and Algorithm Applications

Covers the application of Markov chains and algorithms for function optimization and graph colorings.

Monte Carlo Chain: Motivation and Algorithm

Explores the motivation and algorithm behind the Monte Carlo Chain method.

Set Cover: Integrality Gap

Explores the integrality gap concept in set cover and multiplicative weights algorithms.

Variance Reduction: Strategies and Applications

Discusses variance reduction techniques in stochastic simulation, focusing on allocation strategies and replica generation algorithms.