Capital Theory, Optimal Growth, and Efficiency Conditions with Exhaustible Resources

ε‐Optimal Value and Approximate Multidimensional Dual Dynamic Programming

“…To this effect let Ω = (0, T ) × Ω n −1 with Ω n −1 having a smooth boundary Γ, and distinguish the first variable t 1 in t as time and t 2 , … , t n as space variables. Consider the problem of optimal capital accumulation in a onesectoral economy . The economy has one capital good x ( t ), and n consumption goods C ( t ) = ( C 1 ( t ), … , C n ( t )).…”

“…, tn as space variables. Consider the problem of optimal capital accumulation in a onesectoral economy [23,11]. The economy has one capital good x(t), and n consumption goods C(t) = (C1(t), .…”

“…( , y y t p u y ( , ), )} ≤ −ε ε 0 (11) and satisfying (4) defines a dual e-optimal value, in the way described above. Thus, our aim is to show that if we find in any way (numerically or simply by guess) a Lipschitz continuous function satisfying (11) and (4) then it has to be a dual e-optimal value. In order to calculate an e-optimal pair let us rewrite (11) in terms of the function H from (??)…”

“…Thus, our aim is to show that if we find in any way (numerically or simply by guess) a Lipschitz continuous function satisfying (11) and (4) then it has to be a dual e-optimal value. In order to calculate an e-optimal pair let us rewrite (11) in terms of the function H from (??) and e-dual feedback control ue(t, p) instead of u(t, p):…”

“…Problems of this type find several applications. Only a few are mentioned here: torsion of prismatic bars under elastic as well as elastic‐plastic material laws , the reconstruction of a nonsmooth surface from a pair of stereo images , the analysis of optical flow models , and a deposit problem . Described here is a kind of capital theory as a particular case of –.…”