Now showing items 1-16 of 16

    • Closing the duality gap in linear vector optimization 

      Hamel, AH; Heyde, F; Löhne, A; Tammer, C; Winkler, K (2004)
      Using a set-valued dual cost function we give a new approach to duality theory for linear vector optimization problems. We develop the theory very close to the scalar case. Especially, in contrast to known results, we avoid ...
    • Duality for set-valued measures of risk 

      Hamel, AH; Heyde, F (SIAM PUBLICATIONS, 2010)
      Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531-552] we define set-valued (convex) measures of risk and their acceptance sets, and we give dual representation theorems. A scalarization ...
    • A duality theory for set-valued functions I: Fenchel conjugation theory 

      Hamel, AH (SPRINGER, 2009)
      It is proven that a proper closed convex function with values in the power set of a preordered, separated locally convex space is the pointwise supremum of its set-valued affine minorants. A new concept of Legendre-Fenchel ...
    • Equivalents to Ekeland’s variational principle in uniform spaces 

      Hamel, AH (Elsevier, 2005)
      A minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of [Pacific J. Math. 55(2) (1974) 335–341; Proc. Amer. Math. Soc. 108(3) (1990) 707–714]. Two more equivalent ...
    • A Fenchel-Rockafellar duality theorem for set-valued optimization 

      Hamel, AH (TAYLOR & FRANCIS LTD, 2011)
      A duality theorem of the Fenchel-Rockafellar type for set-valued optimization problems is presented along with a result for the conjugate of the sum of two set-valued functions and a chain rule. The underlying solution ...
    • Lagrange duality in set optimization 

      Hamel, AH; Loehne, A (Springer Verlag (Germany), 2014)
      Based on the complete-lattice approach, a new Lagrangian type duality theory for set-valued optimization problems is presented. In contrast to previous approaches, set-valued versions for the known scalar formulas involving ...
    • Minimal element theorems and Ekeland's principle with set relations 

      Hamel, AH; Löhne, A (YOKOHAMA PUBL, 2006)
      We present two existence principles for minimal points of subsets of the product space X × 2Y, where X stands for a separated uniform space and Y a topological vector space. The two principles are distinct with respect to ...
    • Minimal elements for product orders 

      Hamel, AH; Tammer, C (2008)
      The aim of the present article is to generalize several results of 19 for product spaces X × V, where X is a complete metric space and V is a Banach space and to give considerably simplified proofs. Moreover, we discuss ...
    • A Minty variational principle for set optimization 

      Crespi, GP; Hamel, AH; Schrage, C (Elsevier, 2015)
      Extremal problems are studied involving an objective function with values in (order) complete lattices of sets generated by so called set relations. Contrary to the popular paradigm in vector optimization, the solution ...
    • Notes on extended real- and set-valued functions 

      Hamel, AH; Schrage, C (2012)
      An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving −∞ and/or +∞, so-called residuations. Based on this, ...
    • Phelps’ Lemma, Danes’ Drop theorem and Ekeland’s principle in locally convex spaces 

      Hamel, AH (2003)
      A generalization of Phelps' lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex ...
    • Remarks on the algorithm of Sakawa for optimal control problems 

      Hamel, AH; Benker, H (1998)
      A general optimal control problem for ordinary differential equations is considered. For this problem, some improvements of the algorithm of Sakawa are discussed. We avoid any convexity assumption and show with an example ...
    • Set-valued average value at risk and its computation 

      Hamel, AH; Rudloff, B; Yankova, M (2013)
      New versions of the set-valued average value at risk for multivariate risks are introduced by generalizing the well-known certainty equivalent representation to the set-valued case. The first ’regulator’ version is independent ...
    • Set-valued risk measures for conical market models 

      Hamel, AH; Heyde, F; Rudloff, B (2011)
      Set-valued risk measures on Lpd with 0≤p≤∞ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are ...
    • An ε-lagrange multiplier rule for a mathematical programming problem on Banach spaces 

      Hamel, AH (2001)
      The aim of this paper is to extend the multiplier rule due to Clarke for a nondifferentiable mathematical programming problem on a Banach space to e-minimal (suboptimal) solutions of the problem. This seems to be useful ...