Analysis and optimization, Mathematics

1. In an in finite horizon capital/consumption model, if kt and ct are the capital stock and consumption at time t, we have f(kt) = ct+kt+1 for t ≥ 0 where f is a given production function, and the total utility to be maximized is


where U is a given period utility function and  β ? (0; 1) is a discount factor. Rephrase this as a standard (in finite horizon) control problem and write its Bellman equation.

2. Consider the discrete time control problem:


subject to x0 = x; xt+1 = g(t; xt; ut) for t = 0; : : : ; T - 1 (here f; g are C1, xt; ut ? R, x ? R given). Rewrite this as a Lagrangian optimization problem with 2T +2 variables (x0; : : : ; xT ; u0; : : : ; uT ) and T + 1 constraints. By applying the Lagrange condition to this problem, recover the maximum principle for the control problem (necessary conditions).

3. Consider the problem


subject to the initial and terminal conditions x0 = a; xT = b. One may think of it as a control problem by setting ut = xt+1-xt. Find the minimum and the optimal x *0 ; : : : ; x*T in two ways: directly (eg by Lagrangian method); and by writing the fundamental equation of dynamic programming for and computing Js(x) by backwards induction.


4. Consider the dynamic programming problem with \extended memory":


subject to xt+1 = g(t; xt; xt-1; ut) (x0; x-1 are given). Rephrase as a standard dynamic programming problem (with twice as many state variables).

Posted Date: 2/20/2013 12:54:02 AM | Location : United States

Related Discussions:- Analysis and optimization, Assignment Help, Ask Question on Analysis and optimization, Get Answer, Expert's Help, Analysis and optimization Discussions

Write discussion on Analysis and optimization
Your posts are moderated
Related Questions
Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We

Find reference angle alpha and thea element of [0 degrees, 1800 degrees]

Standard interpretations to derivatives Example   Assume that the amount of money in a bank account is specified by                                       P (t ) = 500 + 10

what are the applications of de moiver''s theorem in programming and software engineering

Find out a series solution for the following differential equation about x 0 = 0 y′′ + y = 0.   Solution Note that in this case p(x)=1 and therefore every point is an or

New England University maintains a data warehouse that stores information about students, courses, and instructors. Members of the university's Board of Trustees are very much inte

how much distance is covered by a man if he is travelling at a speed of 45km/h in 5 sec