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Volumn 66, Issue 1-2, 1996, Pages 239-253

A dimension-reducing method for unconstrained optimization

Author keywords

Bisection method; Dimension reducing method; Imprecise gradient values; Quadratic convergence; Reduction to one dimensional equations; Unconstrained optimization

Indexed keywords

APPROXIMATION THEORY; CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; ITERATIVE METHODS; MATHEMATICAL TRANSFORMATIONS;

EID: 0029709294     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/0377-0427(95)00174-3     Document Type: Article
Times cited : (11)

References (20)
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  • 2
    • 0000476543 scopus 로고
    • Some efficient algorithms for solving systems of nonlinear equations
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  • 3
    • 0040673757 scopus 로고
    • Computer oriented algorithms for solving systems of simultaneous nonlinear algebraic equations
    • G.D. Byrne and C.A. Hall, Eds., Academic Press, New York
    • K.M. Brown, Computer oriented algorithms for solving systems of simultaneous nonlinear algebraic equations, in: G.D. Byrne and C.A. Hall, Eds., Numerical Solution of Systems of Nonlinear Algebraic Equations (Academic Press, New York, 1973).
    • (1973) Numerical Solution of Systems of Nonlinear Algebraic Equations
    • Brown, K.M.1
  • 8
    • 0029532734 scopus 로고
    • A new dimension-reducing method for solving systems of nonlinear equations
    • T.N. Grapsa and M.N. Vrahatis, A new dimension-reducing method for solving systems of nonlinear equations, Internat. J. Comput. Math. 55 (1995) 235-244.
    • (1995) Internat. J. Comput. Math. , vol.55 , pp. 235-244
    • Grapsa, T.N.1    Vrahatis, M.N.2
  • 10
    • 85142184274 scopus 로고    scopus 로고
    • Locating and computing all the simple roots and extrema of a function
    • accepted
    • D. Kavvadias and M.N. Vrahatis, Locating and computing all the simple roots and extrema of a function, SIAM J. Sci. Comput., accepted.
    • SIAM J. Sci. Comput.
    • Kavvadias, D.1    Vrahatis, M.N.2
  • 11
    • 0023406085 scopus 로고
    • A note on solution of nonlinear programming problems with imprecise function and gradient values
    • M. Kupferschmid and J.G. Ecker, A note on solution of nonlinear programming problems with imprecise function and gradient values, Math. Programming Stud. 31 (1987) 129-138.
    • (1987) Math. Programming Stud. , vol.31 , pp. 129-138
    • Kupferschmid, M.1    Ecker, J.G.2
  • 16
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    • Bisection is optimal
    • K. Sikorski, Bisection is optimal, Numer. Math. 40 (1982) 111-117.
    • (1982) Numer. Math. , vol.40 , pp. 111-117
    • Sikorski, K.1
  • 17
    • 0024141611 scopus 로고
    • Solving systems of nonlinear equations using the nonzero value of the topological degree
    • M.N. Vrahatis, Solving systems of nonlinear equations using the nonzero value of the topological degree, ACM Trans. Math. Software 14 (1988) 312-329.
    • (1988) ACM Trans. Math. Software , vol.14 , pp. 312-329
    • Vrahatis, M.N.1
  • 18
    • 0024137570 scopus 로고
    • CHABIS: A mathematical software package for locating and evaluating roots of systems of nonlinear equations
    • M.N. Vrahatis, CHABIS: a mathematical software package for locating and evaluating roots of systems of nonlinear equations, ACM Trans. Math. Software 14 (1988) 330-336.
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  • 19
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    • A short proof and a generalization of Miranda's existence theorem
    • M.N. Vrahatis, A short proof and a generalization of Miranda's existence theorem, Proc. Amer. Math. Soc. 107 (1989) 701-703.
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  • 20
    • 0029689353 scopus 로고    scopus 로고
    • A new unconstrained optimization method for imprecise function and gradient values
    • accepted
    • M.N. Vrahatis, G.S. Androulakis and G.E. Manoussakis, A new unconstrained optimization method for imprecise function and gradient values, J. Math. Anal. Appl., accepted.
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* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.