generalized convexity

On generalized-convex constrained multi-objective optimization

  • Christian Günther
  • Christiane Tammer
    • Categories Constrained Nonlinear Optimization, Generalized Convexity/Monoticity, Multi-Criteria Optimization Tags , , , , ,

    In this paper, we consider multi-objective optimization problems involving not necessarily convex constraints and componentwise generalized-convex (e.g., semi-strictly quasi-convex, quasi-convex, or explicitly quasi-convex) vector-valued objective functions that are acting between a real linear topological pre-image space and a finite dimensional image space. For these multi-objective optimization problems, we show that the set of (strictly, weakly) … Read more

    E. Lieb convexity inequalities and noncommutative Bernstein inequality in Jordan-algebraic setting

  • Leonid Faybusovich
    • Categories Generalized Convexity/Monoticity, Other Topics Tags , ,

    We describe a Jordan-algebraic version of E. Lieb convexity inequalities. A joint convexity of Jordan-algebraic version of quantum entropy is proven. SA spectral theory on semi-simple complex Jordan algebras is used as atool to prove the convexity results. Possible applications to optimization and statistics are indicated CitationPreprint, University of Notre Dame, August 2014ArticleDownload View PDF