Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially in multidimensions. In this article we present a numerical methodology, based upon the Split Bregman L1 minimization technique, that overcomes these challenges, allowing for the fast and accurate computation of 2D TV-based MPLE. We test the methodology with several examples, including V-fold cross-validation with large 2D datasets, and highlight the application of TV-based MPLE to point process crime modeling. The proposed algorithm is implemented as the Matlab function TVMPLE. The Matlab (mex) code and datasets for examples and simulations are available as online supplements.     

一些约束规划问题的近似全局最优解

首先将一个具有多个约束的规划问题转化为一个只有一个约束的规划问题,然后通过利用这个单约束的规划问题,对原来的多约束规划问题提出了一些凸化、凹化的方法,这样这些多约束的规划问题可以被转化为一些凹规划、反凸规划问题．最后,还证明了得到的凹规划和反凸规划的全局最优解就是原问题的近似全局最优解．     

A branch and bound algorithm for scheduling trains in a railway network

The paper studies a train scheduling problem faced by railway infrastructure managers during real-time traffic control. When train operations are perturbed, a new conflict-free timetable of feasible arrival and departure times needs to be re-computed, such that the deviation from the original one is minimized. The problem can be viewed as a huge job shop scheduling problem with no-store constraints. We make use of a careful estimation of time separation among trains, and model the scheduling problem with an alternative graph formulation. We develop a branch and bound algorithm which includes implication rules enabling to speed up the computation. An experimental study, based on a bottleneck area of the Dutch rail network, shows that a truncated version of the algorithm provides proven optimal or near optimal solutions within short time limits.     

最小风险组合证券非负投资比例系数的确定

研究非负投资比例系数约束条件下,实现风险最小化的组合证券投资问题.应用罚函数法,对最小风险组合证券的非负投资比例系数进行研究.实例表明:这一方法是可行的、有效的.     

Solving Sum of Ratios Fractional Programs via Concave Minimization

This article presents an algorithm for globally solving a sum of ratios fractional programming problem. To solve this problem, the algorithm globally solves an equivalent concave minimization problem via a branch-and-bound search. The main work of the algorithm involves solving a sequence of convex programming problems that differ only in their objective function coefficients. Therefore, to solve efficiently these convex programming problems, an optimal solution to one problem can potentially be used to good advantage as a starting solution to the next problem.     

New variants of the generalized level method for minimization of convex nondifferentiable functions taking infinite values

New variants of the generalized level method for minimization of convex Lipschitz functions on a compact set with a nonempty interior are proposed. These variants include the well-known generalized and classical level methods. For the new variants, an estimate of the convergence rate is found, including the variants in which the auxiliary problems are solved approximately.     

A Dual Approach for Solving Nonlinear Infinity-Norm Minimization Problems with Applications in Separable Cases

In this paper,we consider nonlinear infinity-norm minimization problems.We device a reliable Lagrangian dual approach for solving this kind of problems and based on this method we propose an algorithm for the mixed linear and nonlinear infinity- norm minimization problems.Numerical results are presented.     

Entropy resistance analyses of a two-stream parallel flow heat exchanger with viscous heating

Heat exchangers are widely used in industry, and analyses and optimizations of the performance of heat exchangers are important topics. In this paper, we define the concept of entropy resistance based on the entropy generation analyses of a one-dimensional heat transfer process. With this concept, a two-stream parallel flow heat exchanger with viscous heating is analyzed and discussed. It is found that the minimization of entropy resistance always leads to the maximum heat transfer rate for the discussed two-stream parallel flow heat exchanger, while the minimizations of entropy generation rate, entropy generation numbers, and revised entropy generation number do not always.     

How to Extend the Concept of Convexity Cuts to Derive Deeper Cutting Planes

A new type of cutting plane, termed a decomposition cut, is introduced that can be constructed under the same assumptions as the well-known convexity cut. Therefore it can be applied in algorithms (e.g. cutting plane, branch-and-cut) for various problems of global optimization, such as concave minimization, bilinear programming, reverse-convex programming, and integer programming. In computational tests with cutting plane algorithms for concave minimization, decomposition cuts were shown to be superior to convexity cuts.     

Einstein-aether theory with a Maxwell field: General formalism

We extend the Einstein-aether theory to include the Maxwell field in a nontrivial manner by taking into account its interaction with the time-like unit vector field characterizing the aether. We also include a generic matter term. We present a model with a Lagrangian that includes cross-terms linear and quadratic in the Maxwell tensor, linear and quadratic in the covariant derivative of the aether velocity four-vector, linear in its second covariant derivative and in the Riemann tensor. We decompose these terms with respect to the irreducible parts of the covariant derivative of the aether velocity, namely, the acceleration four-vector, the shear and vorticity tensors, and the expansion scalar. Furthermore, we discuss the influence of an aether non-uniform motion on the polarization and magnetization of the matter in such an aether environment, as well as on its dielectric and magnetic properties. The total self-consistent system of equations for the electromagnetic and the gravitational fields, and the dynamic equations for the unit vector aether field are obtained. Possible applications of this system are discussed. Based on the principles of effective field theories, we display in an appendix all the terms up to fourth order in derivative operators that can be considered in a Lagrangian that includes the metric, the electromagnetic and the aether fields.