Direct Search Method Of Quadratic Tridiagonal Interpolation Model

Direct search methods enjoyed great interest amongst both domestic andoverseas researchers between 1960s and 1970s, because it has high demand frompractitioners. Now,it is also high demand that makes the research on the direct searchmethod revive. In the thesis we mainly discuss the algorithms and theory of direct searchmethods,especially of the quadratic tridiagonal interpolation model method.Thestructure of this paper is organized as follows. In the first paper,we survey the history of direct search method, and discuss fourdirect methods respectively,which are simplex method, pattern search method, linesearch method and quadratic interpolation model method.They are currentlyconsidered to be effective methods for unconstrained optimization problems.In eachsection, we discuss the main idea,the development , recent progress and properties ofthese methods. In the second chapter,we develop an quadratic tridiagonal interpolation modelalgorithm for unconstrained optimization,explore its convergent property andcompare its numerical result with the result of general quadratic interpolation modelalgorithm. An the last of the second chapter,we summarize the contents of the above thesechapters and propose some problems in direct search methods that are worthwhile tofurther research.