Search Direction Improvement For
Gradient-based Optimization Problems
Author(s)
S. Ganguly & W. L. Neu
Abstract
Most gradient-based optimization algorithms calculate the search vector using
the gradient or the Hessian of the objective function. This causes the
optimization algorithm to perform poorly in cases where the dimensionality of
the objective function is less than that of the problem. Though some methods
like the Modified Method of Feasible Directions tend to overcome this
shortcoming, they again perform poorly in situations of competing constraints.
This paper introduces a simple modification in the calculation of the search
vector that not only provides significant improvements in the solutions of
optimization problems but also helps to reduce or, in some cases, overcome the
problem of competing constraints.
Keywords: optimization, multidisciplinary design optimization, gradient-based
algorithm, method of feasible directions, search direction.
1 Introduction
An optimization problem can be defined, in terms of a set of decision variables,
X, as:
Minimize Objective Function: ( ),
Subject to: ( ) 0 1... Inequality Constraints,
( ) 0 1... Equality Constraints,
j
k
l u
i i i
g j m
h k l
X X X
≤ ∀ =
= ∀ =
≤ ≤ ∀
X
X
X
F
1... Side Constraints. i n =
(1)
A number of numerical algorithms have been devised to solve this problem.
Gradient-based algorithms are based on the following recursive equation:
1 q q α − = + X X S (2)
where 1 q− X and q X are the vectors of the decision variables in the ( 1)th q − and
the th q iterations respectively. Considering the optimization problem in an
Keywords
optimization, multidisciplinary design optimization, gradient-based
algorithm, method of feasible directions, search direction.
Related Book
Other papers in this volume
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