论文信息 - Variants to the cutting plane approach for convex nondifferentiable optimization

Variants to the cutting plane approach for convex nondifferentiable optimization

We discuss the basic ideas for solving convex nondifferentiable minimization problems through piece wise linear approximations to the objective function. We revise the traditional cutting plane approach by introducing some variants based on suitable translations of the supporting hyperplanes to the epigraph of the function. We describe also some possible choices for defining a quadratic penalty term on the possible displacement to be added to the model. Finally we report on some numerical experiments on standard test problems

M. F. Monaco | M. Gaudioso

[1] L. Zurich,et al. Operations Research in Production Planning, Scheduling, and Inventory Control , 1974 .

[2] C. Lemaréchal. Nonsmooth Optimization and Descent Methods , 1978 .

[3] Manlio Gaudioso,et al. A bundle type approach to the unconstrained minimization of convex nonsmooth functions , 1982, Math. Program..

[4] R. Mifflin. A modification and an extension of Lemarechal’s algorithm for nonsmooth minimization , 1982 .

[5] V. N. Tarasov,et al. A Modification of the Cutting-Plane Method with Accelerated Convergence , 1985 .

[6] R. Fletcher,et al. An algorithm for composite nonsmooth optimization problems , 1986 .

[7] C. Lemaréchal. Nondifferentiable optimization , 1989 .

[8] David Q. Mayne,et al. A superlinearly convergent algorithm for min-max problems , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[9] Krzysztof C. Kiwiel,et al. Proximity control in bundle methods for convex nondifferentiable minimization , 1990, Math. Program..

[10] Manlio Gaudioso,et al. Quadratic approximations in convex nondifferentiable optimization , 1991 .

[11] Krzysztof C. Kiwiel,et al. A tilted cutting plane proximal bundle method for convex nondifferentiable optimization , 1991, Oper. Res. Lett..

[12] Jochem Zowe,et al. A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results , 1992, SIAM J. Optim..