اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدConstructing the Optimal Solutions to the Undiscounted Continuous-Time Infinite Horizon Optimization Problems
223
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We aim to construct the optimal solutions to the undiscounted continuous-time infinite horizon optimization problems, the objective functionals of which may be unbounded. We identify the condition under which the limit of the solutions to the finite horizon problems is optimal for the infinite horizon problems under the overtaking criterion.
قيم البحث
اقرأ أيضاً
We aim to generalize the results of Cai and Nitta (2007) by allowing both the utility and production function to depend on time. We also consider an additional intertemporal optimality criterion. We clarify the conditions under which the limit of the
solutions for the finite horizon problems is optimal among all attainable paths for the infinite horizon problems under the overtaking criterion, as well as the conditions under which such a limit is the unique optimum under the sum-of-utilities criterion. The results are applied to a parametric example of the one-sector growth model to examine the impacts of discounting on optimal paths.
Infinite horizon optimization problems accompany two perplexities. First, the infinite series of utility sequences may diverge. Second, boundary conditions at the infinite terminal time may not be rigorously expressed. In this paper, we show that und
er two fairly general conditions, the limit of the solution to the undiscounted finite horizon problem is optimal among feasible paths for the undiscounted infinite horizon problem, in the sense of the overtaking criterion. Applied to a simple Ramsey model, we show that the derived path contains intriguing properties. We also comprehend the legitimacy of the derived paths by addressing the perplexities with non-standard arguments.
We propose a novel Bayesian method to solve the maximization of a time-dependent expensive-to-evaluate stochastic oracle. We are interested in the decision that maximizes the oracle at a finite time horizon, given a limited budget of noisy evaluation
s of the oracle that can be performed before the horizon. Our recursive two-step lookahead acquisition function for Bayesian optimization makes nonmyopic decisions at every stage by maximizing the expected utility at the specified time horizon. Specifically, we propose a generalized two-step lookahead framework with a customizable emph{value} function that allows users to define the utility. We illustrate how lookahea
We study an optimal stopping problem under non-exponential discounting, where the state process is a multi-dimensional continuous strong Markov process. The discount function is taken to be log sub-additive, capturing decreasing impatience in behavio
ral economics. On strength of probabilistic potential theory, we establish the existence of an optimal equilibrium among a sufficiently large collection of equilibria, consisting of finely closed equilibria satisfying a boundary condition. This generalizes the existence of optimal equilibria for one-dimensional stopping problems in prior literature.
We use the continuation and bifurcation package pde2path to numerically analyze infinite time horizon optimal control problems for parabolic systems of PDEs. The basic idea is a two step approach to the canonical systems, derived from Pontryagins max
imum principle. First we find branches of steady or time-periodic states of the canonical systems, i.e., canonical steady states (CSS) respectively canonical periodic states (CPS), and then use these results to compute time-dependent canonical paths connecting to a CSS or a CPS with the so called saddle point property. This is a (high dimensional) boundary value problem in time, which we solve by a continuation algorithm in the initial states. We first explain the algorithms and then the implementation via some example problems and associated pde2path demo directories. The first two examples deal with the optimal management of a distributed shallow lake, and of a vegetation system, both with (spatially, and temporally) distributed controls. These examples show interesting bifurcations of so called patterned CSS, including patterned optimal steady states. As a third example we discuss optimal boundary control of a fishing problem with boundary catch. For the case of CPS-targets we first focus on an ODE toy model to explain and validate the method, and then discuss an optimal pollution mitigation PDE model.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
