Sentence examples for bundle methods from inspiring English sources

The bundle methods and extragradient methods were extended to equilibrium problems in [6] and [7].

As usual in bundle methods, two cases are considered: the algorithm generates finite number of descent steps; and the algorithm generates infinite number of descent steps.

The first class of algorithms views the problem (1) as the constrained nonsmooth optimization problem, which can be solved directly by several classical nonsmooth methods, such as subgradient methods, bundle methods, and cutting plane methods, Refs. [6 9].

Bundle methods [19 21] are among the most robust and reliable methods to solve general nonsmooth optimization problems, which can be considered stabilized variants of cutting-planes method [14, 15].

We extend the concept of bundle methods to address non-convex and non-smooth optimization problems arising in the design of a feedback control law for the longitudinal flight control of a civil aircraft.

In general, for a convex function h, bundle methods store the trial points (y^{i}), (iin J_{ell}) with their function values and subgradients in a bundle of information: bigcup_{iin J_{ell}} bigl{ bigl y^{i}, hbigl y^{i}bigr), g^{i}_{h} in partial hbigl y^{i}bigr bigr) bigr}, (15) and a point (x^{k}:=x^{k ell)}) (called stability center) which is the "best" point obtained so far.

3, we present the alternating linearization bundle method for problem (1).

Due to the auxiliary problem principle Cohen [15], Salmon et al. [16] developed a bundle method for solving the problem (1.1).

However, we have observed in [9] that a feasible descent bundle method for solving inequality constrained minimax problems is proposed, by using the subgradients of functions, the idea of bundle method and the technique of partial cutting planes model, to generate the new cutting plane and aggregate the subgradients in the bundle, so the difficulty of numerical calculation and storage is overcome.

We introduce a novel random gradient bundle method for approximating local minimizers, motivated by recent work on non-smooth analysis of the function α(X).

Since the bi-level signal control problem is generally a non-convex program, a bundle method using generalized gradients is proposed.