AN N-DIMENSIONAL SEARCH AND OPTIMIZATION PROCEDURE,
Abstract
When a mathematical model of a physical system is constructed, it is often seen to contain a set of N time-invariant independent variables, x to the T power=(x sub 1...x sub i...x sub N). The procedure described enables one to find a value of x to the T power such that f(x)=0, where f(x) is a vector of M functions defined by the system at discrete points. Once the desired behavior is attained, and if N>M, then the procedure will also optimize the system, where the criterion for this optimization is that fo(x), called the payoff function, takes on an extreme value. The behavior of the system is approximated by a first order Taylor series in x. The resulting linear equations are solved for that delta x which produces a minimum sumsquare percentage change in the variables. Once the constraints, f(x)=0, are satisfied, the payoff function is driven to an extremum by demanding successively larger (smaller) values for fo(x). The procedure is an operational computer program. Some of the more salient features of the program discussed include the ability to handle inequality constraints, bounded variables, search convergence rates and optimization sequence logic. Numerical examples and a possible alternate approach to solving the same problems are presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 06, 1963
- Accession Number
- AD0426103
Entities
People
- B. L. Beskind
Organizations
- The Aerospace Corporation