Smoothing a polyhedral convex function via cumulant transformation and homogenization
Annales Polonici Mathematici (1997)
- Volume: 67, Issue: 3, page 259-268
- ISSN: 0066-2216
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] O. Barndorff-Nielsen, Exponential families: exact theory, Various Publ. Ser. 19, Inst. of Math., Univ. of Aarhus, Denmark, 1970. Zbl0249.62006
- [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. Zbl0683.90078
- [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. Zbl0086.01702
- [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. Zbl0401.90089
- [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. Zbl0876.49019
- [8] A. S. Lewis, Convex analysis on the Hermitian matrices, SIAM J. Optim. 6 (1996), 164-177. Zbl0849.15013
- [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. Zbl0911.90277
- [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. Zbl0806.90114
- [11] R. T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, N.J., 1970. Zbl0193.18401
- [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. Zbl0921.49008
- [13] A. Seeger, Convex analysis of spectrally defined matrix functions, SIAM J. Optim. 7 (1997), 679-696. Zbl0890.15018