Approximate Level Method for Nonsmooth Convex Minimization

Journal of Optimization Theory and Applications

Volumn 152, Issue 2, 2012, Pages 334-350

  Richtárik, Peter ^a  

^a UNIVERSITY OF EDINBURGH   (United Kingdom)

Author keywords

Approximate projections in relative scale; Large scale optimization; Level method; Nonsmooth convex minimization; Sensitivity analysis

Indexed keywords

FUNCTIONS; ITERATIVE METHODS; NUMERICAL METHODS; PIECEWISE LINEAR TECHNIQUES;

APPROXIMATE PROJECTION; APPROXIMATE PROJECTION IN RELATIVE SCALE; CONVEX FUNCTIONS; CONVEX MINIMIZATION; FEASIBLE REGIONS; LARGE-SCALE OPTIMIZATION; LEVEL METHOD; NONSMOOTH CONVEX MINIMIZATION; OBJECTIVE FUNCTIONS; PIECEWISE LINEAR MODELS;

SENSITIVITY ANALYSIS;

EID: 84856107006     PISSN: 00223239     EISSN: 15732878     Source Type: Journal    
DOI: 10.1007/s10957-011-9908-1     Document Type: Article

References (16)

1. Kelley, J. E.: The cutting plane method for solving convex programs. J. Soc. Ind. Appl. Math. 8, 703-712 (1960).
2. Nesterov, Y.: Introductory Lectures on Convex Optimization. A Basic Course. Applied Optimization, vol.87. Kluwer Academic, Boston (2004).
3. Lemaréchal, C.: Nonsmooth optimization and descent methods. IIASA Research Report 78-4 (1978).
4. Kiwiel, K. C.: An aggregate subgradient method for nonsmooth convex minimization. Math. Program. 27, 320-341 (1983).
5. Lemaréchal, C., Nemirovskii, A., Nesterov, Y.: New variants of bundle methods. Math. Program. 69(1), 111-147 (1995). doi: 10. 1007/BF01585555.
6. Shor, N. Z.: Minimization Methods for Non-differentiable Functions. Springer Series in Computational Mathematics. Springer, Berlin (1985).
7. Polyak, B. T.: Minimization of unsmooth functionals. U. S. S. R. Comput. Math. Math. Phys. 9(3), 14-29 (1969).
8. Kim, S., Ahn, H., Cho, S. C.: Variable target value subgradient method. Math. Program. 49(1-3), 359-369 (1991). doi: 10. 1007/BF01588797.
9. Kiwiel, K. C.: The efficiency of subgradient projection methods for convex optimization, part I: general level methods. SIAM J. Control Optim. 34, 660-676 (1996).
10. Kiwiel, K. C.: The efficiency of subgradient projection methods for convex optimization, part II: implementations and extensions. SIAM J. Control Optim. 34, 677-697 (1996).
11. Cegielski, A.: A method of projection onto an acute cone with level control in convex minimization. Math. Program. 85(3), 469-490 (1999).
12. Cegielski, A., Dylewski, R.: Residual selection in a projection method for convex minimization problems. Optimization 52, 211-220 (2003). doi: 10. 1080/0233193031000079883.
13. Nesterov, Y.: Unconstrained convex minimization in relative scale. CORE Discussion Paper #2003/96, November (2003).
14. Richtárik, P.: Improved algorithms for convex minimization in relative scale. Tech. rep. (2009).
15. Richtárik, P.: Simultaneously solving seven optimization problems in relative scale. Tech. rep. (2009).
16. Nesterov, Y., Nemirovski, A.: Interior-Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied Mathematics, vol.13. SIAM, Philadelphia (1994).