- Mathematics
- Published 1982

# THE MATHEMATICAL THEORY OF PENALTY FUNCTION METHODS OF OPTIMAL PROCESSES

@inproceedings{Chen1982THEMT, title={THE MATHEMATICAL THEORY OF PENALTY FUNCTION METHODS OF OPTIMAL PROCESSES}, author={Z. Chen}, year={1982} }

In this paper the main contents are:Definition. {p_k(t, x, u)} is called a sequence of exterior (interior) penalty functions, if(1) p_k(·)≥0 and continuous on I×O×U (I×(?)×U), where I=[a, b], open set O(?)R~n, U is a compact convex set of R~r, (?) is the interior of close set B(?)R~n.(2) given any compact set D(?), for each absolutely continuous function x(t)∈D, u(t)∈U, a_1≤t≤b_1, we have(?)integral from n=a_1 to b_1 (p_k(t, x(t), u(t))dt)=0. (1.4)(3) exist closed sets {B_k}:B_(k+1)(?)B_k(?)0… CONTINUE READING