Accession Number : AD0694975

Title :   NEW NECESSARY CONDITIONS OF OPTIMALITY FOR CONTROL PROBLEMS WITH STATE-VARIABLE INEQUALITY CONSTRAINTS.

Descriptive Note : Technical rept.,

Corporate Author : HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS

Personal Author(s) : Jacobson,D. H. ; Lele,M. M. ; Speyer,J. L.

Report Date : AUG 1969

Pagination or Media Count : 43

Abstract : Necessary conditions of optimality for state-variable inequality constrained problems are derived by examining the limiting behavior of the Kelley penalty function technique. The conditions so obtained differ from those presently known, with regard to the behavior of the adjoint variables at junctions of interior and boundary arcs. A second, rigorous, derivation is given; this confirms the necessary conditions obtained by the limiting argument. These conditions are related to those known earlier; in particular, it is shown that the earlier conditions over-specify the behavior of the adjoint variables at the junctions. An example is used to demonstrate that the earlier conditions may yield non-stationary trajectories. For the regular case, it is shown that, under certain conditions, only boundary points, as opposed to boundary arcs, are possible. An analytic example illustrates this behavior. (Author)

Descriptors :   (*CONTROL SYSTEMS, *MATHEMATICAL PROGRAMMING), NONLINEAR PROGRAMMING, FUNCTIONAL ANALYSIS, CALCULUS OF VARIATIONS, PARTIAL DIFFERENTIAL EQUATIONS, NUMERICAL ANALYSIS, OPTIMIZATION, INEQUALITIES, THEOREMS

Subject Categories : Theoretical Mathematics
      Operations Research

Distribution Statement : APPROVED FOR PUBLIC RELEASE