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ABIN1 is a polyubiquitin-binding protein known to regulate NF-κB activation and cell death signaling. Mutations in Abin1 can cause severe immune diseases in human, such as psoriasis, systemic lupus erythematosus, and systemic sclerosis. Here, we generated mice that disrupted the ubiquitin-binding domain of ABIN1 (Abin1

When using interior point methods for solving semidefinite programs (SDP), one needs to solve a system of linear equations at each iteration. For problems of large size, solving the system of linear equations can be very expensive. In this paper, we propose a trust region algorithm for solving SDP problems. At each iteration we perform a number of conjugate gradient iterations, but do not need to solve a system of linear equations. Under mild assumptions, the convergence of this algorithm is established. Numerical examples are given to illustrate the convergence results obtained.

Index tracking problems are concerned in this paper. A CVaR risk constraint is introduced into general index tracking model to control the downside risk of tracking portfolios that consist of a subset of component stocks in given index. Resulting problem is a mixed 0–1 and non-differentiable linear programming problem, and can be converted into a mixed 0–1 linear program so that some existing optimization software such as CPLEX can be used to solve the problem. It is shown that adding the CVaR constraint will have no impact on the optimal tracking portfolio when the index has good (return increasing) performance, but can limit the downside risk of the optimal tracking portfolio when index has bad (return decreasing) performance. Numerical tests on Hang Seng index tracking and FTSE 100 index tracking show that the proposed index tracking model is effective in controlling the downside risk of the optimal tracking portfolio.

The global optimization method based on discrete filled function is a new method that solves large scale max-cut problems. We first define a new discrete filled function based on the structure of the max-cut problem and analyze its properties. Unlike the continuous filled function methods, by the characteristic of the max-cut problem, the parameters in the proposed filled function does not need to be adjusted. By combining a procedure that randomly generates initial points for minimization of the proposed filled function, the proposed algorithm can greatly reduce the computational time and be applied to large scale max-cut problems. Numerical results and comparisons with several heuristic methods indicate that the proposed algorithm is efficient and stable to obtain high quality solution of large scale max-cut problems.

Chen and Tseng (Math Program 95:431–474, 2003) extended non-interior continuation methods for solving linear and nonlinear complementarity problems to semidefinite complementarity problems (SDCP), in which a system of linear equations is exactly solved at each iteration. However, for problems of large size, solving the linear system of equations exactly can be very expensive. In this paper, we propose a version of one of the non-interior continuation methods for monotone SDCP presented by Chen and Tseng that incorporates inexactness into the linear system solves. Only one system of linear equations is inexactly solved at each iteration. The global convergence and local superlinear convergence properties of the method are given under mild conditions.

Two kinds of MAX RES CUT problems, the MAX s−t CUT and the MAX s−t−v CUT, with limited unbalanced constraints are considered. Approximation algorithms used in Frieze and Jerrum (Integer Programming and Combinatorial Optimization, vol. 920, pp. 1–13, Springer, Berlin, 1995), Galbiati and Maffioli (Theor. Comput. Sci. 385:78–87, 2007), Han et al. (Math. Program. Ser. B 92:509–535, 2002) and Ye (Math. Programm. 90:101–111, 2001) are extended to the two MAX RES CUT problems. A special matrix P is constructed by which it can ensure that the given nodes s,t are feasible to equality constraints with probability one for the MAX s−t CUT and s,t,v are feasible to equality constraints with at least probability 0.912 for the MAX s−t−v CUT. A fussy greedy sizing-adjusted procedure is then proposed to confirm that the round solution is feasible for all constraints. We find these extensions are nontrivial and some interesting results about performance ratio are obtained for the MAX RES CUT problem with limited unbalanced constraints.

This paper presents an infeasible-interior-point algorithm for a class of nonmonotone complementarity problems, and analyses its convergence and computational complexity. The results indicate that the proposed algorithm is a polynomial-time one.

In this paper, we propose a 2-step trust region indefinite dogleg path method for the solution of nonlinear equality constrained optimization problems. The method is a globally convergent modification of the locally convergent Fontecilla method and an indefinite dogleg path method is proposed to get approximate solutions of quadratic programming subproblems even if the Hessian in the model is indefinite. The dogleg paths lie in the null space of the Jacobian matrix of the constraints. An l1 exact penalty function is used in the method to determine if a trial point is accepted. The global convergence and the local two-step superlinear convergence rate are proved. Some numerical results are presented.

In this paper, we propose a class of convenient curvilinear search algorithms to solve trust region problems arising from unconstrained optimization. The curvilinear paths we set are dogleg paths, generated mainly by employing Bunch‐Parlett factorization for general symmetric matrices which may be indefinite. These algorithms are easy to use and globally convergent. It is proved that these algorithms satisfy the first‐ and second‐order stationary point convergence properties and that the convergence rate is quadratic under commonly used conditions.