353. Set-valued IFS for the Analysis of Iterative Methods in Non-Convex Optimization
Invited abstract in session WC-6: Advances in monotone inclusions and related methods, stream Methods for non-/monotone inclusions and their applications.
Wednesday, 10:05 - 11:20Room: M:H
Authors (first author is the speaker)
| 1. | Allahkaram Shafiei
|
| Computer Science, Czech Technical University |
Abstract
In the domain of non-convex optimization, dissecting the behavior and convergence characteristics of iterative methods is essential yet challenging due to the complexity of the objective functions. This study presents a novel strategy employing set-valued iterated function systems (IFS) to examine such methods. Set-valued IFS offers a structured framework to model the dynamic behavior of iterative algorithms, effectively tracking the evolution of solution sets throughout iterations. Let us consider a stochastic dynamical system in the form of a ground set, a family of maps from elements of the ground set to subsets of the ground set, and a probability function that suggests the probability of each map within the family. This generalizes the iterated function systems (IFS) to set-valued maps. In this setting, we present several novel conditions for the existence of a unique invariant measure of convergence of iterated random compositions of such maps. Within this paper, we examine innovative stochastic reformulations of the non-convex feasibility problem aimed at enhancing the advancement of novel algorithmic methodologies. So, by this method, we are inspired to solve non-convex feasibility problems refer to a class of optimization problems where the goal is to find a point (or set of points) that satisfies a given set of constraints, but the feasible region defined by these constraints is non-convex.
Keywords
- Convex and non-smooth optimization
- Optimization under uncertainty and applications
- Linear and nonlinear optimization
Status: accepted
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