Bao Q. Truong

Subdifferentials and SNC property of scalarization functionals with uniform level sets and applications

  • Christiane Tammer
  • Bao Q. Truong
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization, Nonsmooth Optimization

    This paper deals with necessary conditions for minimal solutions of constrained and unconstrained optimization problems with respect to general domination sets by using a well-known nonlinear scalarization functional with uniform level sets (called Gerstewitz’ functional in the literature). The primary objective of this work is to establish revised formulas for basic and singular subdifferentials of … Read more

    Variational Analysis and Applications to Group Dynamics

  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , ,

    In this paper, we establish a new version of Ekeland’s variational principle in a new setting of cone pseudo-quasimetric spaces. In constrast to metric spaces, we do not require that each forward Cauchy sequence is forward convergent and that each forward convergent sequence has the unique forward limit. The motivation of this paper comes from … Read more

    Variational principles, completeness and the existence of traps in behavioral sciences

  • Stephan Cobzas
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - Science and Engineering, Nonlinear Optimization

    In this paper, driven by Behavioral applications to human dynamics, we consider the characterization of completeness in pseudo-quasimetric spaces in term of a generalization of Ekeland’s variational principle in such spaces, and provide examples illustrating significant improvements to some previously obtained results, even in complete metric spaces. At the behavioral level, we show that the … Read more

    Variational principles with generalized distances and applications to behavioral sciences

  • Phan Q. Khanh
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Global Optimization, Nonsmooth Optimization Tags , , , , ,

    This paper has a two-fold focus on proving that the quasimetric and the weak $\tau$-distance versions of the Ekeland variational principle are equivalent in the sense that one implies the other and on presenting the need of such extensions for possible applications in the formation and break of workers hiring and firing routines. ArticleDownload View … Read more

    Minimal Points, Variational Principles, and Variable Preferences in Set Optimization

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Nonlinear Optimization

    The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point … Read more

    Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we first develop two new results of variational analysis. One is a fixed point theorem for parametric dynamic systems in quasimetric spaces, which can also be interpreted as an existence theorem of minimal points with respect to reflexive and transitive preferences for sets in products spaces. The other one is a variational … Read more

    Variational analysis in psychological modeling

  • Boris S. Mordukhovich
  • Antoine Soubeyran
  • Bao Q. Truong
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , , , ,

    This paper develops some mathematical models arising in psychology and some other areas of behavioral sciences that are formalized via general preferences with variable ordering structures. Our considerations are based on the recent “variational rationality approach” that unifies numerous theories in different branches of behavioral sciences by using, in particular, worthwhile change and stay dynamics … Read more