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Extremal types for certain \(L^ p \)minimization problems and associated large scale nonlinear programs. (English) Zbl 0515.49022


MSC:

49M37 Numerical methods based on nonlinear programming
90C52 Methods of reduced gradient type
49M15 Newton-type methods
65K05 Numerical mathematical programming methods
90C30 Nonlinear programming
52A20 Convex sets in \(n\) dimensions (including convex hypersurfaces)
52Bxx Polytopes and polyhedra
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References:

[1] Dunn JC (1979) Rates of convergence for conditional gradient algorithms near singular and nonsingular extremals. SIAM J Contr Opt 17:187-211 · Zbl 0403.49028 · doi:10.1137/0317015
[2] Dunn JC (1980) Convergence rates for conditional gradient sequences generated by implicit step length rules. SIAM J Contr Opt 18:473-487 · Zbl 0457.65048 · doi:10.1137/0318035
[3] Cannon MD, Cullum CD (1968) A tight upper bound on the rate of convergence of the Frank-Wolfe algorithm. SIAM J Contr Ser A 6:509-516 · Zbl 0186.24002 · doi:10.1137/0306032
[4] Dunn JC (1981) Global and asymptotic convergence rate estimates for a class of projected gradient processes. SIAM J Contr Opt 19:368-400 · Zbl 0488.49015 · doi:10.1137/0319022
[5] Dunn JC (1980a) Newton’s method and the Goldstein step length rule for constrained minimization problems. SIAM J Contr Opt 18:659-674 · Zbl 0445.90098 · doi:10.1137/0318050
[6] Hughes GC (1981) Convergence rate analysis for iterative minimization schemes with quadratic subproblems. PhD dissertation. Mathematics Department, North Carolina State University
[7] Pontryagin LS, Boltyanskii VG, Gamkrelidze RV, Mischenko EF (1962) The mathematical theory of optimal processes. Interscience, New York
[8] Haynes G, Hermes H (1963) Nonlinear control problems with control appearing linearly. SIAM J Contr Opt Ser A 1:85-108 · Zbl 0145.12602
[9] Valentine FA (1964) Convex sets. McGraw-Hill, New York · Zbl 0129.37203
[10] Rockafellar RT (1970) Convex analysis. Princeton University Press, Princeton NJ · Zbl 0193.18401
[11] Gawande M, Hedges, J (1981) Private communication.
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