帰納法と微分方程式を使う最適化

最近二つの問題を解きながら以上の課題を触りました。
Differential equations were used for deducing that
x'(t) = Ax(t) can be solved to yield
x(t) = (e^(At))x(0) where A is a matrix.
The problem is to find the vector x(0) which produces the optimal (c,x(T)) subject to initial constraint (c,x(0))<=B, given A, T,c, and B.

Induction was used to prove that the greedy approach to solving an algorithm problem was optimal. Basically, the problem is to find the largest number of turns in a game of removing cards from a deck where, if card i is removed, i+1 and i-1 are also removed, if either of them is in the deck. My algorithm, on each turn, selects the card to remove which affects the fewest others.