An extension of davidon methods to non differentiable problems

Abstract

Making use of convex analysis a property possessed by almost all Davidon methods is exhibited. This property--although true only in the quadratic case~oes not depend on the quadratic nature of the objective function. An algorithm is given which is shown to coincide with the conjugate gradient algorithm in the quadratic case. The convergence is proven when applied to uniformly convex functions. Numerical aspects are considered.

Scheduling of Intelligent and Autonomous Vehicles under pairing/unpairing collaboration strategy in container terminals

“…Very similar methods has been also proposed in Held and Karp (1971) for solving traveling salesman problem. Later, Lemarechal (1975) proposed the well-known bundle methods as an extension to the subgradient. The volume algorithm was proposed in Barahona and Anbil (2000) as a methods which simultaneously produces a primal feasible solution for the problem and a further analysis of its relation with bundle methods is reported in Bahiense et al (2002).…”

Nonsmooth optimization and robust control

“…For computational minimization of nonsmooth convex functions, bundle methods (Lemaréchal, 1975) have proven highly effective. The bundle idea has been extended to nonconvex functions (Kiwiel, 1985;Schramm & Zowe, 1992;Vlček & Lukšan, 2001), although implementation is very delicate, and publicly available code is scarce.…”

Méthode du sous-gradient réduit généralisé comme extension du GRG d'Abadie au cas non différentiable

“…Toutes les méthodes de sous-gradient utilisent le principe de perturbation des sous-différentiels et des dérivées directionnelles pour garantir la convergence à des solutions e-optimales comme le cas de Lemaréchal [12], Wolf e [26] et Bihain, Nguyen et Strodiot [2].…”