Tutorial on Surrogate Constraint Approaches for Optimization in Graphs

Surrogate constraint methods have been embedded in a variety of mathematical programming applications over the past thirty years, yet their potential uses and underlying principles remain incompletely understood by a large segment of the optimization community. In a number of significant domains of combinatorial optimization, researchers have produced solution strategies without recognizing that they can be derived as special instances of surrogate constraint methods. Once the connection to surrogate constraint ideas is exposed, additional ways to exploit this framework become visible, frequently offering opportunities for improvement.We provide a tutorial on surrogate constraint approaches for optimization in graphs, illustrating the key ideas by reference to independent set and graph coloring problems, including constructions for weighted independent sets which have applications to associated covering and weighted maximum clique problems. In these settings, the surrogate constraints can be generated relative to well-known packing and covering formulations that are convenient for exposing key notions. The surrogate constraint approaches yield widely used heuristics for identifying independent sets as simple special cases, and also afford previously unidentified heuristics that have greater power in these settings. Our tutorial also shows how the use of surrogate constraints can be placed within the context of vocabulary building strategies for independent set and coloring problems, providing a framework for applying surrogate constraints that can be used in other applications.At a higher level, we show how to make use of surrogate constraint information, together with specialized algorithms for solving associated sub-problems, to obtain stronger objective function bounds and improved choice rules for heuristic or exact methods. The theorems that support these developments yield further strategies for exploiting surrogate constraint relaxations, both in graph optimization and integer programming generally.     

非线性非完整约束空间准坐标表示的系统的基本动力学方程

用与准坐标表示的一阶非线性非完整约束超曲面的基矢量共线的量和米歇尔斯基方程点来作为一阶非线性非完整约束变质量系统的基本动力学方程．由此可导出用准坐标表示的各种形式的运动微分方程．和约登（Jourdain）原理相容．举了例子．     

An Analysis of Partially Clairvoyant Scheduling

Real-time scheduling problems confront two issues not addressed by traditional scheduling models, viz., parameter variability and the existence of complex relationships constraining the executions of jobs. Accordingly, modeling becomes crucial in the specification of scheduling problems in such systems. In this paper, we analyze scheduling algorithms in Partially Clairvoyant Real-time scheduling systems and present a new dual-based algorithm for the feasibility problem in the case of strict relative constraints. We also study the problem of online dispatching in Partially Clairvoyant systems and show that the complexity of dispatching is logarithmically related to the complexity of the schedulability problem.     

可行逐步二次规划方法解非线性方程组

We transform the system of nonlinear equations into a nonlinear programming problem, which is attacked by feasible sequential quadratic programming(FSQP) method.We do not employ standard least square approach.We divide the equations into two groups. One group, which contains the equations with zero residual,is treated as equality constraints. The square of other equations is regarded as objective function. Two groups are updated in every step.Therefore, the subproblem is updated at every step, which avoids the difficulty that it is required to lie in feasible region for FSQP.     

The Gradient Projection Method with Exact Line Search

The gradient projection algorithm for function minimization is often implemented using an approximate local minimization along the projected negative gradient. On the other hand, for some difficult combinational optimization problems, where a starting guess may be far from a solution, it may be advantageous to perform a nonlocal (exact) line search. In this paper we show how to evaluate the piece-wise smooth projection associated with a constraint set described by bounds on the variables and a single linear equation. When the NP hard graph partitioning problem is formulated as a continuous quadratic programming problem, the constraints have this structure.     

两不同部件串联可修系统的可用度的一个新的计算方法

本用直接解一组不含时间t的一阶线性偏微分积方程而得到两不同部件可修系统的可用度。     

An acquisition policy for a single item multi-supplier system with real-world constraints

This paper proposes an exact acquisition policy for solving the single-item multi-supplier problem with real-world constraints. Compared with the model of Rosenblatt et al. [Note. An acquisition policy for a single item multi-supplier system, Manage. Sci. 44 (1998) S96–S100], the proposed method has contributions in that the global optimal solutions can be obtained to indicate the best acquisition policy, and real-world constraints can easily be added as appropriate for real-world situations. In addition, the benefits of price-quantity discount (PQD) under conditions of the single item muti-supplier system are also considered in the paper.