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A Linear Scalarization Proximal Point Method for Quasiconvex Multiobjective Minimization
- Publication Year :
- 2015
-
Abstract
- In this paper we propose a linear scalarization proximal point algorithm for solving arbitrary lower semicontinuous quasiconvex multiobjective minimization problems. Under some natural assumptions and using the condition that the proximal parameters are bounded we prove the convergence of the sequence generated by the algorithm and when the objective functions are continuous, we prove the convergence to a generalized critical point. Furthermore, if each iteration minimize the proximal regularized function and the proximal parameters converges to zero we prove the convergence to a weak Pareto solution. In the continuously differentiable case, it is proved the global convergence of the sequence to a Pareto critical point and we introduce an inexact algorithm with the same convergence properties. We also analyze particular cases of the algorithm obtained finite convergence to a Pareto optimal point when the objective functions are convex and a sharp minimum condition is satisfied.<br />The main motivation to study this problem are the consumer demand theory in economy, where the quasiconvexity of the objective vector function is a natural condition associated to diversication of the consumption,. arXiv admin note: text overlap with arXiv:1403.0150
- Subjects :
- TheoryofComputation_MISCELLANEOUS
Control and Optimization
Applied Mathematics
Proximal point method
Pareto principle
Management Science and Operations Research
Critical point (mathematics)
Proximal point
Quasiconvex function
Optimization and Control (math.OC)
Bounded function
Theory of computation
FOS: Mathematics
Applied mathematics
Minification
Mathematics - Optimization and Control
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....3cec32b1bcf4defd8691fc32f4d09b6a