A globally convergent modified version of the method of moving asymptotes

A new modified moving asymptotes method is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and explicitly solved. In doing so we propose a strategy to incorporate a modified second-order information for the moving asymptotes location. Under natural assumptions, we prove the geometrical convergence. In addition the experimental results reveal that the present method is significantly faster compared to the [1] method, Newton's method and the BFGS Method.

Uncovering Specific-Shape Graph Anomalies in Attributed Graphs

As networks are ubiquitous in the modern era, point anomalies have been changed to graph anomalies in terms of anomaly shapes. However, the specific-shape priors about anomalous subgraphs of interest are seldom considered by the traditional approaches when detecting the subgraphs in attributed graphs (e.g., computer networks, Bitcoin networks, and etc.). This paper proposes a nonlinear approach to specific-shape graph anomaly detection. The nonlinear approach focuses on optimizing a broad class of nonlinear cost functions via specific-shape constraints in attributed graphs. Our approach can be used to many different graph anomaly settings. The traditional approaches can only support linear cost functions (e.g., an aggregation function for the summation of node weights). However, our approach can employ more powerful nonlinear cost functions, and enjoys a rigorous theoretical guarantee on the near-optimal solution with the geometrical convergence rate.

A globally convergent modified version of the method of moving asymptotes

A new modified moving asymptotes method is presented. In each step of the iterative process, a strictly convex approximating subproblem is generated and explicitly solved. In doing so we propose a strategy to incorporate a modified second-order information for the moving asymptotes location. Under natural assumptions, we prove the geometrical convergence. In addition the experimental results reveal that the present method is significantly faster compared to the [1] method, Newton's method and the BFGS Method.