Logarithmic Quasi-distance Proximal Point Scalarization Method for Multi-Objective Programming
Abstract
Recently, Greg\'orio and Oliveira developed a proximal point scalarization method (applied to multi-objective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this study, a variation of this method is proposed, using the regularization with logarithm and quasi-distance, which entails losing important properties, such as convexity and differentiability. However, proceeding differently, it is shown that any sequence \{(x^k, z^k)\} \includ R^n \times R^{m}_{++} generated by the method satisfies: \{z^k\} is convergent and \{x^k\} is bounded and its accumulation points are weak pareto solutions of the unconstrained multi-objective optimization problem
Cite
@article{arxiv.1305.1592,
title = {Logarithmic Quasi-distance Proximal Point Scalarization Method for Multi-Objective Programming},
author = {Rogério Azevedo Rocha and Paulo Roberto Oliveira and Ronaldo Gregório},
journal= {arXiv preprint arXiv:1305.1592},
year = {2013}
}
Comments
The importance of multi-objective optimization can be seen from the large variety of applications presented in the literature. White [28] offers a bibliography of 504 papers describing various different applications addressing, for example, problems concerning agriculture, banking, health services, energy, industry and water