Nonlinear coordinate representations of smooth optimization problems

摘要: Nonlinear coordinate representations of smooth optimization problems are investigated from the point view variable metric algorithms. In other words, nonlinear systems, in sense differential geometry, studied by taking into consideration structure and methods. Both unconstrained constrained cases discussed. The present approach is based on fact that transformation an problem can be replaced a suitable Riemannian belonging to Euclidean class. case equality inequality constraints, these questions related closely right inverses full-rank matrices; therefore, their characterization starting analysis. main results concern new subclass transformations connection with common supply coordinates two manifolds, one immersed one. This situation corresponds differentiable manifold improves insight theoretical background For wide class methods, convergence theorem invariant form (not depending representations) proved. Finally, convexification image studied.