On Critical Point for Functions with Bounded Parameters

Abstract

Selection of descent direction at a point plays an important role in numerical optimizationfor minimizing a real valued function. In this article, a descent sequence is generated for the functions with bounded parameters to obtain a critical point. First, sufficient condition for the existence of descent direction is studied for this function and then a set of descent directions at a point is determined using linear expansion. Using these results a descent sequence of intervals is generated and critical point is characterized. This theoretical development is justified with numerical example.keywords Line search technique, Markov difference, Interval ordering, Descent direction, Critical point.

Existence of solution of constrained interval optimization problems with regularity concept

“…Conventional optimization techniques cannot be applied directly to solve ( CP) since the interval space is not linearly ordered. There are numerous studies in this direction over the years dealing with linear [8-10, 13, 18, 27] and nonlinear [11,14,15,21] interval optimization models in both single and multi objective cases. Most of these methods follow a common process, which transforms ( CP) to a general optimization problem through different scalarization techniques and determines the upper and lower bound of the objective function.…”