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Optimization
A Journal of Mathematical Programming and Operations Research
Volume 60, 2011 - Issue 3
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Original Articles

Randomized Hessian estimation and directional search

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Pages 329-345 | Received 25 Sep 2008, Accepted 20 May 2009, Published online: 29 Mar 2010

References

  • Akaike , H . 1959 . On a successive transformation of probability distribution and its application to the analysis of the optimum gradient method . Ann. Inst. Stat. Math. , 11 : 1 – 16 .
  • Billingsley , P . 1986 . Probability and Measure , New York : John Wiley & Sons .
  • Brodlie , KW . 1975 . A new direction set method for unconstrained minimization without evaluating derivatives . J. Inst. Math. Appl. , 15 : 385 – 396 .
  • Ermoliev , Yu and Wets , RJ-B . 1988 . Numerical Techniques for Stochastic Optimization , Berlin : Springer-Verlag .
  • Gaviano , M . 1975 . “ Some general results on convergence of random search algorithms in minimization problems ” . In Towards Global Optimisation , Edited by: Dixon , LCW and Szego , GP . 149 – 157 . London : North-Holland .
  • Luo , ZQ and Tseng , P . 1992 . On the convergence of the coordinate descent method for convex differentiable minimization . J. Optim. Theory Appl. , 72 : 7 – 35 .
  • Nazareth , L . 1976 . Generation of conjugate directions for unconstrained minimization without derivatives . Math. Comput. , 30 ( 133 ) : 115 – 131 .
  • Powell , MJD . 1964 . An efficient method for finding the minimum of a function of several variables without calculating derivatives . Comput. J. , 7 : 155 – 162 .
  • Powell , MJD . 1973 . On search directions for minimization algorithms . Math. Progr. , 4 : 193 – 201 .
  • Rappl , G . 1989 . On linear convergence of a class of random search algorithms . ZAMM – J. Appl. Math. Mech. , 69 ( 1 ) : 37 – 45 .
  • Solis , FJ and Wets , RJ-B . 1981 . Minimization by random search techniques . Math. Oper. Res. , 6 ( 1 ) : 19 – 30 .
  • Spall , JC . 2003 . Introduction to Stochastic Search and Optimization: Estimation, Simulation and Control , New York : John Wiley & Sons .
  • Zangwill , WI . 1967 . Minimizing a function without calculating derivatives . Comput. J. , 10 ( 3 ) : 293 – 296 .

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