Stochastics Perturbations of Global Optimization. Analysis and Applications

      Аннотация: In this book, the global optimization of a nonconvex objective function is studied via stochastic perturbation. Stochastic perturbation is a method for the transformation of local minimization procedures in to global ones in the framework of continuous optimization. We have considered a general problem of unconstrained continuous and linear constraints optimization where the objective function may be nonsmooth. Standard meth-ods for smooth functions usually generate a descent direction by using the gradient and may be extended to nonsmooth situations by using a generalized gradient instead of the standard one whenever it is necessary. For instance, Clarke’s generalized gradients may be used at the points where the objective function is not differentiable. According to this observation, we have considered a variable metric descent method and introduced suitable affine local approximations to be used. The projected variable metric descent method is considered for continuous optimization with linear constraints, and we have considered generalized reduced gradient (GRG) for nonlinear constraints optimization where the objective function is twice differentiable.

Ключевые слова: Integer Programming, Active Set Method, Multi-objective optimization, Nonsmooth Optimization, Penalty Function, stochastic perturbation, Reduced Gradient Method and its Generalization, Nonconvex Optimization, Variable Metric Method.