The Ψ-transform for solving linear and non-linear programming problems

✍ Scribed by V.K. Chichinadze

• Publisher: Elsevier Science
• Year: 1969
• Tongue: English
• Weight: 710 KB
• Volume: 5
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(69)90076-4

✦ Synopsis

The global extremum value, as well as its coordinates, of a non-linear multidimensional objective function may be found approximately, but practically, as the zero value of its transformation, a monotonically decreasing scalar function. Summary--This paper is concerned with the problem of determining the global extremum value of a multidimensional, non-linear objective function which may have several extreme values. The problem is solved by transforming the objective function, through a particular ~ transformation, into a function W (~) of one new variable (~). The value of this transformed function is shown to decrease continuously to zero as the value of this new variable is increased, and the value of the variable when the transformed function equals zero is the global extremum of the original objective function. Methods of calculating the transformed function are discussed and examples of the technique are given. It is shown that the values of the system coordinates corresponding to the global extremum can also be determined.