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A DC piecewise affine model and a bundling technique in nonconvex nonsmooth minimization. (English) Zbl 1211.90182
Summary: We introduce an algorithm to minimize a function of several variables with no convexity nor smoothness assumptions. The main peculiarity of our approach is the use of an objective function model which is the difference of two piecewise affine convex functions. Bundling and trust region concepts are embedded into the algorithm. Convergence of the algorithm to a stationary point is proved and some numerical results are reported.

MSC:
90C26 Nonconvex programming, global optimization
65K05 Numerical mathematical programming methods
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[1] DOI: 10.1137/0806013 · Zbl 0846.65028
[2] Mäkelä M., Nonsmooth Optimization (1992)
[3] DOI: 10.1137/0802008 · Zbl 0761.90090
[4] Lemaréchal C., Optimization and Operations Research, Vol. 117 of Lecture Notes in Economics and Mathematical Systems pp pp. 191–199– (1976)
[5] Fuduli A., SIAM Journal on Optimization (2003)
[6] Demyanov V.F., Constructive Nonsmooth Analysis (1995) · Zbl 0887.49014
[7] Clarke F., Optimization and Nonsmooth Analysis (1983) · Zbl 0582.49001
[8] DOI: 10.1007/BF01386389 · Zbl 0113.10703
[9] Kelley J.E., Journal of SIAM 8 pp 703– (1960)
[10] DOI: 10.1137/0314056 · Zbl 0358.90053
[11] Hiriart-Urruty J.B., Convex Analysis and Minimization Algorithms (1993) · Zbl 0795.49001
[12] DOI: 10.1287/moor.2.2.191 · Zbl 0395.90069
[13] Outrata G., Nonsmooth approach to optimization problems with equilibrium constraints. Theory, Applications and Numerical Results (1998)
[14] DOI: 10.1007/BF02591907 · Zbl 0525.90074
[15] Lukšan L. Vlček J. (2000) Test problems for nonsmooth unconstrained and linearly constrained optimization Tech. Report 798 Institute of Computer Science, Academy of Sciences of the Czech Republic Prague pp. 1–34
[16] DOI: 10.1023/A:1011990503369 · Zbl 1029.90060
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