| This thesis introduces the nondiffenrentiable optimization theory and algorithm, including history of the development, research signification, application areas and study status quo. Propose the concept of circumscribe cuboid in the bicompact convex set and construct a circumscribe cuboid in a subdifferentiable set. On this basis a class of nondiffenrentiable optimization algorithm is given to solve the unconstrained problem. The algorithm is different from the current methods. The sure for search direction do not require calculate subdifferentiable set and any order subgradient, and solve any two-order programming. It simply computes 2n directional derivatives. The convergence of the algorithm is also proof. The paper proves several integral median theorems and the linear convergence of the algorithm under certain conditions through the introduction of the concept of second directional derivative. For the characteristics of max function, the account ofε-subgradient of max function is given, and then a class of algorithm is gained to resolve a minimax problem and the convergence of the algorithm is proof. By numerical experiment for the two types of function, the numerical results show that the given algorithm is feasible and effective, and has the characteristics of large-scale convergence. Compare with the existing nondiffenrentiable optimization algorithm, our algorithm has the advantages of fast convergence and iterative fewer. Especially, for the function provided with rigorous nondiffenrentiable point and the minimax problem, our algorithm has the even obvious advantages. Finally, linear classification problems are converted to a class of unconstrained optimization problem. And the thesis present a numerical method for calculate subgradient, then to solve linear classification problems by use of the subgradient algorithm. Examples show that the nondiffenrentiable optimization algorithm for linear regression equation is simple and practical.
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