Directional Lipschitzian optimal solution of infinite-dimensional optimization problems

infinite dimensional garch models

مدلهای گارچ در فضاهای هیلبرت پایان نامه حاضر شامل دو بخش می باشد. در قسمت اول مدلهای اتورگرسیو تعمیم یافته مشروط به ناهمگنی واریانس در فضاهای هیلبرت را معرفی، مفاهیم ریاضی مورد نیاز در تحلیل این مدلها در دامنه زمان را مطرح کرده و آنها را مورد بررسی قرار می دهیم. بر اساس پیشرفتهایی که اخیرا در زمینه تئوری داده های تابعی و آماره های عملگری ایجاد شده است، فرآیندهایی که دارای مقادیر در فضاهای ...

Double smoothing technique for infinite-dimensional optimization problems with applications to optimal control

In this paper, we propose an efficient technique for solving some infinite-dimensional problems over the sets of functions of time. In our problem, besides the convex point-wise constraints on state variables, we have convex coupling constraints with finite-dimensional image. Hence, we can formulate a finite-dimensional dual problem, which can be solved by efficient gradient methods. We show th...

Chapter 4 Optimal Control Problems in Infinite Dimensional Function

In this chapter, we will consider optimal control problems in function space where we will restrict ourselves to state equations that are both linear in the state and linear in the control: We assume that E is a reflexive, separable Banach space with norm ‖ · ‖E and dual space E∗ and X is another separable Banach space with norm ‖ · ‖X and separable dual space X∗. We further suppose A : D(A) ⊆ ...

Lecture Notes, 285J Infinite-dimensional Optimization and Optimal Design

A Finite Algorithm for Solving Infinite Dimensional Optimization Problems

We consider the general optimization problem (P ) of selecting a continuous function x over a σ -compact Hausdorff space T to a metric space A, from a feasible region X of such functions, so as to minimize a functional c on X. We require that X consist of a closed equicontinuous family of functions lying in the product (over T ) of compact subsets Yt of A. (An important special case is the opti...