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

617_equationa.png

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:

1882_equationb.png

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

850_equationc.png

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.

1264_equationd.png

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

1507_equatione.png

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
Levels of significance A level of significance is a probability value which is utilized when conducting tests of hypothesis. A level of significance is mostly the probability

Determine the eigenvalues and eigenvectors of the subsequent matrix. Solution : The first thing that we require to do is determine the eigen-values. It means we require

Truth Criteria :  Consider the following statements: i) Peahens (i.e., female peacocks) lay eggs around September. ii) Water boils at 100°C. iii) 5 divides 15 without lea

Explain how to Converting Percents to Decimals ? Percent : "Percent" means "per hundred." Percents are represented by a percent sign ( % ) to the right of a number.  For exam

Center and Radius 1)(x+2)^2-(y-3)^2=4


my question involves frequencies less than five and i cannot aggregate the data, what do i use instead of the chi-square test?

how many times In a 12 hour period will he numbers add up to 6? (hint 3:00 is one answer0

Prove that a reaction following the rate law v = k[A] 2 is characterized by a linear plot of [P] t 1 versus t-l, where P is the product of the stoichiometric reaction A = P. Sho

Write each of the given radicals in exponent form. Solution As illustrated in the last two parts of this example we have to be careful with parenthesis.  While we