Necessary conditions for a multistage bolza- mayer problem involving control variables and having inequality and finite equation constraints

A multiplier rule and analogues of the Weierstrass and Clebsch conditions are developed for a multistage Bolza-Meyer calculus of variations problems. The number of stages is fixed, but partition points defining state boundaries are variable. Discontinuities are allowed in variables finite equations and inequalities, as well as differential equations, all of which involve control variables.

An appendix summarizes some of the results obtained by C. H. Denbow, as modified by R. W. hunt, for a generalized Bolza problem. The appendix is independent of the rest of the paper.