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Full-Text Articles in Physical Sciences and Mathematics
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
Variational Analysis Of Marginal Functions With Applications To Bilevel Programming, Boris S. Mordukhovich, Nguyen Mau Nam, Hung M. Phan
Mathematics Research Reports
This paper pursues a twofold goal. First to derive new results on generalized differentiation in variational analysis focusing mainly on a broad class of intrinsically nondifferentiable marginal/value functions. Then the results established in this direction apply to deriving necessary optimality conditions for the optimistic version of bilevel programs that occupy a remarkable place in optimization theory and its various applications. We obtain new sets of optimality conditions in both smooth and smooth settings of finite-dimensional and infinite-dimensional spaces.
Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr
Applications Of Variational Analysis To A Generalized Heron Problem, Boris S. Mordukhovich, Nguyen Mau Nam, Juan Salinas Jr
Mathematics Research Reports
This paper is a continuation of our ongoing efforts to solve a number of geometric problems and their extensions by using advanced tools of variational analysis and generalized differentiation. Here we propose and study, from both qualitative and numerical viewpoints, the following optimal location problem as well as its further extensions: on a given nonempty subset of a Banach space, find a point such that the sum of the distances from it to n given nonempty subsets of this space is minimal. This is a generalized version of the classical Heron problem: on a given straight line, find a point …