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1997 | 67 | 3 | 259-268
Tytuł artykułu

Smoothing a polyhedral convex function via cumulant transformation and homogenization

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a polyhedral convex function g: ℝⁿ → ℝ ∪ {+∞}, it is always possible to construct a family ${gₜ}_{t>0}$ which converges pointwise to g and such that each gₜ: ℝⁿ → ℝ is convex and infinitely often differentiable. The construction of such a family ${gₜ}_{t>0}$ involves the concept of cumulant transformation and a standard homogenization procedure.
Rocznik
Tom
67
Numer
3
Strony
259-268
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-04-02
poprawiono
1996-10-17
Twórcy
  • Department of Mathematics, University of Avignon, 33, Rue Louis Pasteur, 84000 Avignon, France
Bibliografia
  • [1] O. Barndorff-Nielsen, Exponential families: exact theory, Various Publ. Ser. 19, Inst. of Math., Univ. of Aarhus, Denmark, 1970.
  • [2] A. Ben-Tal and M. Teboulle, A smoothing technique for nondifferentiable optimization problems, in: Lecture Notes in Math. 1405, S. Dolecki (ed.), Springer, Berlin, 1989, 1-11.
  • [3] D. Bertsekas, Constrained Optimization and Lagrangian Multiplier Methods, Academic Press, New York, 1982.
  • [4] C. Davis, All convex invariant functions of hermitian matrices, Arch. Math. (Basel) 8 (1957), 276-278.
  • [5] R. A. El-Attar, M. Vidyasagar, and S. R. K. Dutta, An algorithm for l₁-norm minimization with application to nonlinear l₁-approximation, SIAM J. Numer. Anal. 16 (1979), 70-86.
  • [6] R. Ellis, Entropy, Large Deviations and Statistical Mechanics, Springer, Berlin, 1985.
  • [7] C. Lemaréchal and C. Sagastizábal, Practical aspects of the Moreau-Yosida regularization: theoretical preliminaries, SIAM J. Optim. 7 (1997), 367-385.
  • [8] A. S. Lewis, Convex analysis on the Hermitian matrices, SIAM J. Optim. 6 (1996), 164-177.
  • [9] J. E. Martinez-Legaz, On convex and quasiconvex spectral functions, in: Proc. 2nd Catalan Days on Appl. Math., M. Sofonea and J. N. Corvellec (eds.), Presses Univ. de Perpignan, Perpignan, 1995, 199-208.
  • [10] M. L. Overton and R. S. Womersley, Optimality conditions and duality theory for minimizing sums of the largest eigenvalues of symmetric matrices, Math. Programming 62 (1993), 321-357.
  • [11] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970.
  • [12] A. Seeger, Smoothing a nondifferentiable convex function: the technique of the rolling ball, Technical Report 165, Dep. of Mathematical Sciences, King Fahd Univ. of Petroleum and Minerals, Dhahran, Saudi Arabia, October 1994.
  • [13] A. Seeger, Convex analysis of spectrally defined matrix functions, SIAM J. Optim. 7 (1997), 679-696.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-apmv67z3p259bwm
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