96 publications from this institution
The paper is devoted to establishing relationships between global and local monotonicity, as well as their maximality versions, for single-valued and set-valued mappings between finite-dimensional and infinite-dimensional spaces. We first show that for single-valued operators with convex domains in locally convex topological spaces, their continuity ensures that their global monotonicity agrees with the local one around any point of the graph. This also holds for set-valued mappings defined on the real line under a certain connectedness condition. The situation is different for set-valued operators in multidimensional spaces as demonstrated by an example of locally monotone operator on the plane that is not globally monotone. Finally, we invoke coderivative criteria from variational analysis to characterize both global and local maximal monotonicity of set-valued operators in Hilbert spaces to verify the equivalence between these monotonicity properties under the closed-graph and global hypomonotonicity assumptions.
In this special issue, we take the opportunity, on the occasion of his 65th birthday, to acknowledge the outstanding contributions of Professor Alexander Kruger (home page: https://asterius.ballara...
This paper is focused on some properties of paramonotone operators on Banach spaces and their application to certain feasibility problems for convex sets in a Hilbert space and convex systems in the Euclidean space. In particular, it shows that operators that are simultaneously paramonotone and bimonotone are constant on their domains, and this fact is applied to tackle two particular situations. The first one, closely related to simultaneous projections, deals with a finite amount of convex sets with an empty intersection and tackles the problem of finding the smallest perturbations (in the sense of translations) of these sets to reach a nonempty intersection. The second is focused on the distance to feasibility; specifically, given an inconsistent convex inequality system, our goal is to compute/estimate the smallest right-hand side perturbations that reach feasibility. We advance that this work derives lower and upper estimates of such a distance, which become the exact value when confined to linear systems.
We present a model of learning in which agents learn from errors. If an action turns out to be an error, the agent rejects not only that action but also neighboring actions. We find that, keeping memory of his errors, under mild assumptions an acceptable solution is asymptotically reached. Moreover, one can take advantage of big errors for a faster learning.
In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.
The classic Voronoi cells can be generalized to a higher-order version by considering the cells of points for which a given $k$-element subset of the set of sites consists of the $k$ closest sites. We study the structure of the $k$-order Voronoi cells and illustrate our theoretical findings with a case study of two-dimensional higher-order Voronoi cells for four points.
Higle, J. L. and Sen, S. (eds.), Stochastic Decomposition. A Statistical Method for Large Scale Stochastic Linear Programming. Kluwer Academic Publ., Dordrecht. Boston. London 1996, 248 pp., $112.00, ISBN 0-7923-3840-5. Horst, R., Pardalos, P. M. and Thoai, N. V., Introduction to Global Optimization. Nonconvex Optimization and its Applications 3. Kluwer Academic Publ., Dordrecht. Boston. London 1995, 318 pp., & HB 109.00, ISBN 0-7923-3556-2; f PB 46.00, ISBN 0-7923-3557-0 Ledyard, J. 0 . (ed.), The Economics of Informational Decentralization: Complexity, Efficiency and Stability. Essays in Honor of Stanley Reiter. Kluwer Academic Publ., Dordrecht. Boston. London 1995, 456 pp., & 129.25, ISBN 0-7923-9502-6. Mizrahi, A., Sullivan, M., Finite Mathematics. An Applied Approach. Seventh Edition. J. Wiley & Sons New York, Chichester, Brisbane, Toronto, Singapore 1996, 599 pp. and 53 pp. Appendix, £ 23, 50, ISBN 0-47 1 - 10700-X.
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