The continuous-time problem with interval-valued functions: applications to economic equilibrium

The aim of this paper is to define the Continuous-Time Problem in an interval context and to obtain optimality conditions for this problem. In addition, we will find relationships between solutions of Interval Continuous-Time Problem and Interval Variational-like Inequality Problems, both Stampacchi...

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Bibliographic Details
Published in:Optimization methods & software 2019-11, Vol.34 (6), p.1123-1144
Main Authors: Ruiz-Garzón, G., Osuna-Gómez, R., Rufián-Lizana, A., Chalco-Cano, Y.
Format: Article
Language:English
Subjects:
Banach spaces
continuous-time programming problems
economic application
Equilibrium
Interval analysis
Mathematical programming
multiobjective optimization
variational-like inequality problem
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Summary:The aim of this paper is to define the Continuous-Time Problem in an interval context and to obtain optimality conditions for this problem. In addition, we will find relationships between solutions of Interval Continuous-Time Problem and Interval Variational-like Inequality Problems, both Stampacchia and Minty type. Pseudo invex monotonicity condition ensures the existence of solutions of the problem. These results generalize similar conclusions obtained in Euclidean or Banach spaces inside classical mathematical programming problems or Continuous-Time Problems. We will finish generalizing the existence of Walrasarian equilibrium price model and the Wardrop's principle for traffic equilibrium problem to an environment of interval-valued functions.
ISSN:1055-6788
1029-4937
DOI:10.1080/10556788.2018.1464569