Convergence analysis of an infeasible quasi- Newton bundle method for nonsmooth convex programming

By utilizing the improvement function,we change the nonsmooth convex constrained optimization into an unconstrained optimization,and construct an infeasible quasi-Newton bundle method with proximal form.It should be noted that the objective function being minimized in unconstrained optimization subproblem may vary along the iterations(it does not change if the null step is made,otherwise it is updated to a new function).It is necessary to make some adjustment in order to obtain the convergence result.We employ the main idea of infeasible bundle method of Sagastizabal and Solodov,and under the circumstances that each iteration point may be infeasible for primal problem,we prove that each cluster point of the sequence generated by the proposed algorithm is the optimal solution to the original problem.Furthermore,for BFGS quasi-Newton algorithm with strong convex objective function,we obtain the condition which guarantees the boundedness of quasi-Newton matrices and the R-linear convergence of the iteration points.

Comparison of Morphological and Genetic Differentiations in Filial Generation of Cross Between Indica and Japonica Rice

A recombinant inbred line （RIL） population of F8 and F9 generations derived from a cross between a typical indica rice （Qishanzhan） and a typical japonica rice （Akihikari） was used to study the difference between morphological differentiation based on phenotype characters and genetic differentiation using indica and japonica specific SSR markers, and to evaluate the relationship between vascular bundle characters and morphological and genetic differentiations. The results showed that the frequency distributions of morphological and genetic differentiations were all inclined to japonica type in the filial generation. The population was more inclined to japonica type based on genetic differentiation than on morphological differentiation. The consistent degrees of classification based on the Cheng’s index, the ratio of large vascular bundle number to small vascular bundle number in panicle neck （RLSVB） and the ratio of large vascular bundle number in the second internode from the top to that in the panicle neck （RLVB） were all about 50% compared with the genetic differentiation, and the consistent degree of the total scores of the Cheng’s index combined with the vascular bundle number ratios was significantly increased to about 80% compared with the genetic differentiation. Therefore, the vascular bundle characters could be used as a helpful supplement for subspecies classification.

A DECOMPOSITION METHOD FOR CONVEX MINIMIZATION PROBLEMS AND ITS APPLICATION

In this paper, we present a modified decomposition algorithm and its bundle style variant for convex programming problems with separable structure. We prove that these methods are globally and linearly convergent and discuss the application of the bundle variant in parallel computations.

Nonsmooth identification of mechanical systems with backlash-like hysteresis

Backlash-like hysteresis is one of the nonsmooth and multi-valued nonlinearities usually existing in mechanical systems. The traditional identification method is quite difficult to be used to model the systems involved with such complex nonlinearities. In this paper, a nonsmooth recursive identification algorithm for the systems with backlash-like hysteresis is proposed. In this method, the concept of Clarke subgradient is introduced to approximate the gradients at nonsmooth points and the so-called bundle method is used to obtain the optimization search direction in nonsmooth cases. Then, a recursive algorithm based on the idea of bundle method is developed for parameter estimation. After that, the convergence analysis of the algorithm is investigated. Finally, simulation results to validate the proposed method on a simulated mechanical transmission system are presented.