Optimization of equations with nonlinear constraints: comparison between heuristic and convex techniques
Jose Jose Barba-Ortega
Published 2022-03-23
Keywords
- spatial convex,
- metaheuristic techniques,
- convex extraction,
- Cholezky Factorization,
- Echelon Factorization
- Schur Factorization,
- Moment matrices ...More
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Copyright (c) 2022 Revista UIS Ingenierías
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Abstract
In this article, different optimization techniques were explored through different methodologies. It is important to highlight that optimization problems are found in a large number of academic disciplines and the paths proposed to solve them are found first in the so-called strong mathematical techniques (global optimum) through existence and uniqueness theorems, and the second way, the so-called heuristic or metaheuristic techniques, inspired mostly by biological, social, and cultural processes which allow expanding the search spaces for solutions or relaxing the functions to be optimized from continuous to non-continuous as well as constraints. The metaheuristic technique studied is the particle swarm optimization, (PSO) based on the complete model (cognitive and social components) which is a metaheuristic technique inspired by biology, comparatively with the convex mathematical technique using the behavior of positive semi-definite matrices, for the formulation and modeling of problems with objective functions and convex feasible regions. The problem solved by these two methods consists of knowing the values of the resources of two variables within an objective function. Finally, the answers obtained are evaluated under the assumption that the local minima are global minima within the neighborhood.
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