Smoothing technique and its applications in semidefinite optimization

Mathematical Programming

Volumn 110, Issue 2, 2007, Pages 245-259

  Nesterov, Yurii ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Black box model; Complexity theory; Convex optimization; Non smooth optimization; Optimal methods; Smoothing technique; Structural optimization

Indexed keywords

CONSTRAINED OPTIMIZATION; EIGENVALUES AND EIGENFUNCTIONS; ITERATIVE METHODS; LINEAR MATRIX INEQUALITIES; MATHEMATICAL MODELS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING;

BLACK-BOX MODEL; COMPLEXITY THEORY; CONVEX OPTIMIZATION; NON-SMOOTH OPTIMIZATION; SMOOTHING TECHNIQUES;

STRUCTURAL OPTIMIZATION;

EID: 33947732413     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-006-0001-8     Document Type: Article

References (10)

1. Helmberg, C., Rendl, F.: A spectral bundle method for semidenite programming. In: Technical Report SC 97-37, Konrad-Zuse-Zentrum fur Informationstechnik Berlin 1997
2. Helmberg, C., Oustry, F.: Bundle methods to minimize the maximum eigenvalue function. In: Vandenberghe, R. Saigal, H. Wolkovicz, (eds.) Hanbook on semidefinite programming. Theory, algorithms and applications. Kluwer Dordrecht 1999
3. Lemarechal, C., Oustry, F.: Nonsmooth algorithms to solve semidefinite programs. In: El Ghaoui, L. Niculescu S.I. (eds.) Recent advances on LMI methods in control. Advances in design and control series. SIAM 1999
4. Lewis, A.S., Sendov, H.S.: Twice differentiable spectral functions. SIMAX 23(2), 368-386 (2001)
5. Nayakkankuppam, M.V., Tymofejev, Y.: A parallel implementation of the spectral bundle method for large-scale semidefinite programs. In: Proceedings of the 8th SIAM conference on applied linear algebra, Williamsburg (VA) 2003
6. Nemirovskii, A.S., Yudin, D.B.: Problem complexity and method efficiency in optimization. Wiley, New York 1983
7. Nesterov, Yu.: Introductory lectures on convex optimization. A basic course. Kluwer, Boston 2004
8. Nesterov, Yu.: Smooth minimization of non-smooth functions. Mathematical programming, 103(1), 127-152 (2005)
9. Nesterov, Yu.: Excessive gap technique in nonsmooth convex minimization. SIAM J Optim 16(1), 235-249 (2005)
10. Nesterov, Yu.: Unconstrained convex minimization in relative scale. CORE Discussion Paper 2003/96 (2003)