Journal Of The Econometric Society

An International Society for the Advancement of Economic
Theory in its Relation to Statistics and Mathematics

Edited by: Guido W. Imbens • Print ISSN: 0012-9682 • Online ISSN: 1468-0262

Econometrica: Jul, 1966, Volume 34, Issue 3

Maximization by Quadratic Hill-Climbing<541:MBQH>2.0.CO;2-K
p. 541-551

Hale F. Trotter, Richard E. Quandt, Stephen M. Goldfeld

The purpose of this paper is to describe a new gradient method for maximizing general functions. After a brief discussion of various known gradient methods the mathematical foundation is laid for the new algorithm which rests on maximizing a quadratic approximation to the function on a suitably chosen spherical region. The method requires no assumptions about the concavity of the function to be maximized and automatically modifies the step size in the lifet of the success of the quadratic approximation to the function. The paper further discusses some practical problems of implementing the algorithm and presents recent computational experience with it.

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