Browsing Articles  Economics and Management by Author "Hamel, AH"
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Benson type algorithms for linear vector optimization and applications
Hamel, AH; Löhne, A; Rudloff, B (2013) 
Closing the duality gap in linear vector optimization
Hamel, AH; Heyde, F; Löhne, A; Tammer, C; Winkler, K (2004)Using a setvalued 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 setvalued measures of risk
Hamel, AH; Heyde, F (SIAM PUBLICATIONS, 2010)Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531552] we define setvalued (convex) measures of risk and their acceptance sets, and we give dual representation theorems. A scalarization ... 
A duality theory for setvalued 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 setvalued affine minorants. A new concept of LegendreFenchel ... 
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 FenchelRockafellar duality theorem for setvalued optimization
Hamel, AH (TAYLOR & FRANCIS LTD, 2011)A duality theorem of the FenchelRockafellar type for setvalued optimization problems is presented along with a result for the conjugate of the sum of two setvalued functions and a chain rule. The underlying solution ... 
Lagrange duality in set optimization
Hamel, AH; Loehne, A (Springer Verlag (Germany), 2014)Based on the completelattice approach, a new Lagrangian type duality theory for setvalued optimization problems is presented. In contrast to previous approaches, setvalued 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 setvalued 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 +∞, socalled 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 wellknown 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 ... 
Setvalued average value at risk and its computation
Hamel, AH; Rudloff, B; Yankova, M (2013)New versions of the setvalued average value at risk for multivariate risks are introduced by generalizing the wellknown certainty equivalent representation to the setvalued case. The first ’regulator’ version is independent ... 
Setvalued risk measures for conical market models
Hamel, AH; Heyde, F; Rudloff, B (2011)Setvalued 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 superhedge a multivariate claim are ... 
An εlagrange 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 eminimal (suboptimal) solutions of the problem. This seems to be useful ...