A combinatorial batch code has strong practical motivation in the distributed storage and retrieval of data in a database. In this survey, we give a brief introduction to the combinatorial batch codes and some progress.

Determining the search direction and the search step are the two main steps of the nonlinear optimization algorithm, in which the derivatives of the objective and constraint functions are used to determine the search direction, the one-dimensional search and the trust domain methods are used to determine the step length along the search direction. One dimensional line search has been widely discussed in various textbooks and references. However, there is a less-known technique—arc-search method, which is relatively new and may generate more efficient algorithms in some cases. In this paper, we will survey this technique, discuss its applications in different optimization problems, and explain its potential improvements over traditional line search method.

In many fields, we need to deal with hierarchically structured data. For this kind of data, hierarchical mixed effects model can show the correlation of variables in the same level by establishing a model for regression coefficients. Due to the complexity of the random part in this model, seeking an effective method to estimate the covariance matrix is an appealing issue. Iterative generalized least squares estimation method was proposed by Goldstein in 1986 and was applied in special case of hierarchical model. In this paper, we extend the method to the general hierarchical mixed effects model, derive its expressions in detail and apply it to economic examples.

Let p and q be two distinct odd primes and let d=(p-1,q-1). In this paper, we construct d-ary generalized two-prime Sidelnikov sequences and study the autocorrelation values and linear complexity.

In this paper, a new infinite-dimensional necklace Lie algebra is studied and the left and right index arrays of a necklace word in necklace Lie algebra is first defined. Using the left and right index arrays, we divide the necklace words into 5 classes. We discuss finite-dimensional Lie subalgebras of necklace Lie algebras intensively and prove that some subalgebras are isomorphism to simple Lie algebra sl\left(n\right).

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 Sagastizàbal 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.