Generalized Convexity/Monoticity

Convex- and Monotone- Transformable Mathematical Programming Problems and a Proximal-Like Point Method

  • João Xavier da Cruz Neto
  • Orizon Pereira Ferreira
  • L. R. Lucambio Pérez
  • S. Z. Nemeth
    • Categories Constrained Nonlinear Optimization, Generalized Convexity/Monoticity, Global Optimization Theory Tags , ,

    The problem of finding singularities of monotone vectors fields on Hadamard manifolds will be considered and solved by extending the well-known proximal point algorithm. For monotone vector fields the algorithm will generate a well defined sequence, and for monotone vector fields with singularities it will converge to a singularity. It will be also shown how … Read more

    Optimality Conditions for Vector Optimization with Set-Valued Maps

  • Yongwei Huang
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , , ,

    Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary … Read more