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Riemannian manifold optimality conditions for nonsmooth optimization studies

Author: FuWeiWei
Tutor: GaoLeiFu
School: Liaoning Technical University
Course: Applied Mathematics
Keywords: Riemannian manifold Nonsmooth optimization Optimality conditions Generalized Directional Derivative Generalized Gradient Convex analysis
CLC: O186.12
Type: Master's thesis
Year: 2009
Downloads: 58
Quote: 1
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Abstract


Research on Riemannian manifolds nonsmooth problems and related issues has been one of the hot issues of optimization , some scholars put several important nonsmooth analysis tool from the Euclidean space is extended to the Riemannian manifold . This innovative in Riemannian manifold given Lipschitz function Penot generalized directional derivative concept , the use of Penot generalized directional derivative and the Clarke generalized gradient given Riemannian manifold unconstrained nonsmooth optimization necessary conditions , first-order and second-order sufficient condition the flat space of Lagrange theorem promotion, use of manifold given the nature of the need for equality constrained optimization problem conditions , and through the non-smooth exact penalty function approach would inequality constrained optimization problem into unconstrained problem , with the penalty function given its necessary optimality conditions . Convex analysis theory is an important theoretical basis of mathematical programming , this paper discussed earlier Riemannian manifold basis, additional geodesic convex function of the basic conditions , the contents of the theory of convex analysis and conclusions parallel to the Riemannian manifold promotion. With geodesic convex unconstrained optimization problems demonstrate the necessary and sufficient conditions , and on this basis, the depth given equality constrained optimization problems, and inequality constrained optimization problem with equality and inequality constraints optimization problems necessary optimality conditions proved a theorem of classical Lagrange multiplier unity conclusions.

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Differential geometry,integral geometry > Differential Geometry > Riemannian geometry
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