Journal of Optimization Theory and Applications

, Volume 28, Issue 3, pp 429–434

On the convergence of the LJ search method

Authors

  • G. Gopalakrishnan Nair
    • Department of MathematicsCollege of Engineering
Technical Note

DOI: 10.1007/BF00933384

Cite this article as:
Gopalakrishnan Nair, G. J Optim Theory Appl (1979) 28: 429. doi:10.1007/BF00933384

Abstract

The convergence of the Luus-Jaakola search method for unconstrained optimization problems is established.

Key Words

Optimal search techniquesconvergence proofssufficient conditionsCantor's intersection theorem

Notation

En

Euclideann-space

f

Gradient off(x)

2f

Hessian matrix

(·)T

Transpose of (·)

I

Index set {1, 2, ...,n}

[xi1*(j)]

Point around which search is made in the (j + 1)th iteration, i.e., [x1l*(j),x2l*(j),...,xn1*(j)]

ri(i)

Range ofxil*(i) in the (j + 1)th iteration

l1

min {ri(0)}

l2

min {ri(0)}

Aj

Region of search in thejth iteration, i.e., {x εEn:xil*(j-1)−0.5ri(j-1)xixil*(j-1)+0.5ri(j-1),i εI}

Sαj

Closed sphere with center origin and radiusαj

ɛ

Reduction factor in each iteration

θ

1−ɛ

Γ(·)

Gamma function

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Copyright information

© Plenum Publishing Corporation 1979