45 research outputs found
Measuring the balance space sensitivity in vector optimization
Recent literature has shown that the balance space approach may be a significant a1ternative to address several topics concerning vector optimization. Although this new look also leads lo the eflicient set and, consequently, is equivalent to the classical viewpoint, it yields new results and a1gorithms, as well as new economic interpretations, that may be very useful in theoretical framevorks and practical applications. The present paper focuses on the sensitivity of The balance set. We prove a general envelope theorem that yields the sensitivity with respect to any parameter considered in the problem. Fulthermore, we provide a dual problem that characlerizes the primal balance space and its sensitivity. Finally, we a1so give the implications of our results with respect to the sensitivity of the efficient set
Sensitivity in Multiobjective Programming by Differential Equations Methods. The Case of Homogeneous Functions
Proceedings of the Second International Conference on Multi-Objective Programming and Goal Programming, Torremolinos, Spain, May 16-18, 1996.The purpose of this paper is to characterize for convex multiobjective programming, the situations in which the sensitivity with respect to the right side vector of the constraints can be obtained as a solution of a dual program.Publicad
Set optimization - a rather short introduction
Recent developments in set optimization are surveyed and extended including
various set relations as well as fundamental constructions of a convex analysis
for set- and vector-valued functions, and duality for set optimization
problems. Extensive sections with bibliographical comments summarize the state
of the art. Applications to vector optimization and financial risk measures are
discussed along with algorithmic approaches to set optimization problems
Recent progress in random metric theory and its applications to conditional risk measures
The purpose of this paper is to give a selective survey on recent progress in
random metric theory and its applications to conditional risk measures. This
paper includes eight sections. Section 1 is a longer introduction, which gives
a brief introduction to random metric theory, risk measures and conditional
risk measures. Section 2 gives the central framework in random metric theory,
topological structures, important examples, the notions of a random conjugate
space and the Hahn-Banach theorems for random linear functionals. Section 3
gives several important representation theorems for random conjugate spaces.
Section 4 gives characterizations for a complete random normed module to be
random reflexive. Section 5 gives hyperplane separation theorems currently
available in random locally convex modules. Section 6 gives the theory of
random duality with respect to the locally convex topology and in
particular a characterization for a locally convex module to be
prebarreled. Section 7 gives some basic results on convex
analysis together with some applications to conditional risk measures. Finally,
Section 8 is devoted to extensions of conditional convex risk measures, which
shows that every representable type of conditional convex risk
measure and every continuous type of convex conditional risk measure
() can be extended to an type
of lower semicontinuous conditional convex risk measure and an
type of continuous
conditional convex risk measure (), respectively.Comment: 37 page