The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application.     

基于种群分类排序的约束优化遗传算法

针对约束优化问题,提出了一类将种群中的个体分类排序的思想.算法的特点在于:先将种群中的解分为可行解和不可行解两类,然后分别按照不同的标准排序.由于很多约束优化问题的最优解位于可行域的边界上或附近,所以排序时并不认为可行解一定优于不可行解.基于此分类排队思想,特别设计了只允许同等级个体进行交叉的新的交叉算子,称之为同等级交叉算子,以及基于一维搜索的变异算子.算法同时采用了保证固定比例不可行解的自适应策略.4个标准测试函数的数值仿真结果验证了算法的有效性.     

Optimal boundary feedback stabilization of a string with moving boundary

Email: gugat{at}am.uni-erlangen.de Received on April 30, 2006; We consider a finite string that is fixed at one end and subjectto a feedback control at the other end which is allowed to move.We show that the behaviour is similar to the situation whereboth ends are fixed: As long as the movement is not too fast,the energy decays exponentially and for a certain parameterin the feedback law it vanishes in finite time. We considermovements of the boundary that are continuously differentiablewith a derivative whose absolute value is smaller than the wavespeed. We solve a problem of worst-case optimal feedback control,where the parameter in the feedback law is chosen such thatthe worst-case L^p-norm of the space derivative at the fixedend of the string is minimized (p [1, )). We consider the worstcase both with respect to the initial conditions and with respectto the boundary movement. It turns out that the parameter forwhich the energy vanishes in finite time is optimal in thissense for all p.     

Numerical Experience with a Reduced Hessian Method for Large Scale Constrained Optimization

The reduced Hessian SQP algorithm presented in Biegler et al. [SIAM J. Optimization, Vol. 5, no. 2, pp. 314–347, 1995.] is developed in this paper into a practical method for large-scale optimization. The novelty of the algorithm lies in the incorporation of a correction vector that approximates the cross term Z^TWYp_Y. This improves the stability and robustness of the algorithm without increasing its computational cost. The paper studies how to implement the algorithm efficiently, and presents a set of tests illustrating its numerical performance. An analytic example, showing the benefits of the correction term, is also presented.     

On the Smoothing of the Square-Root Exact Penalty Function for Inequality Constrained Optimization

In this paper we propose two methods for smoothing a nonsmooth square-root exact penalty function for inequality constrained optimization. Error estimations are obtained among the optimal objective function values of the smoothed penalty problem, of the nonsmooth penalty problem and of the original optimization problem. We develop an algorithm for solving the optimization problem based on the smoothed penalty function and prove the convergence of the algorithm. The efficiency of the smoothed penalty function is illustrated with some numerical examples, which show that the algorithm seems efficient.     

解非线性优化问题的锥模型信赖域方法

Trust region methods are powerful and effective optimization methods. The conic model method is a new type of method with more information available at each iteration than standard quadratic-based methods. The advantages of the above two methods can be combined to form a more powerful method for constrained optimization. The trust region subproblem of our method is to minimize a conic function subject to the linearized constraints and trust region bound. At the same time, the new algorithm still possesses robust global properties. The global convergence of the new algorithm under standard conditions is established.     

On convergence analysis of a derivative-free trust region algorithm for constrained optimization with separable structure

In this paper,we propose a derivative-free trust region algorithm for constrained minimization problems with separable structure,where derivatives of the objective function are not available and cannot be directly approximated.At each iteration,we construct a quadratic interpolation model of the objective function around the current iterate.The new iterates are generated by minimizing the augmented Lagrangian function of this model over the trust region.The filter technique is used to ensure the feasibility and optimality of the iterative sequence.Global convergence of the proposed algorithm is proved under some suitable assumptions.     

On two actuarial quantities for the compound Poisson risk model with tax and a threshold dividend strategy

In this paper, we consider a compound Poisson risk model with taxes paid according to a loss-carry-forward system and dividends paid under a threshold strategy. First, the closed-form expression of the probability function for the total number of taxation periods over the lifetime of the surplus process is derived. Second, analytical expression of the expected accumulated discounted dividends paid between two consecutive taxation periods is provided. In addition, explicit expressions are also given for the exponential individual claims.     

Optimal investment for the defined-contribution pension with stochastic salary under a CEV model

In this paper, we study the optimal investment strategy of defined-contribution pension with the stochastic salary. The investor is allowed to invest in a risk-free asset and a risky asset whose price process follows a constant elasticity of variance model. The stochastic salary follows a stochastic differential equation, whose instantaneous volatility changes with the risky asset price all the time. The HJB equation associated with the optimal investment problem is established, and the explicit solution of the corresponding optimization problem for the CARA utility function is obtained by applying power transform and variable change technique. Finally, we present a numerical analysis.     

Optimal control of an elastic crane-trolley-load system - a case study for optimal control of coupled ODE-PDE systems

We present a mathematical model of a crane-trolley-load model, where the crane beam is subject to the partial differential equation (PDE) of static linear elasticity and the motion of the load is described by the dynamics of a pendulum that is fixed to a trolley moving along the crane beam. The resulting problem serves as a case study for optimal control of fully coupled partial and ordinary differential equations (ODEs). This particular type of coupled systems arises from many applications involving mechanical multi-body systems. We motivate the coupled ODE-PDE model, show its analytical well-posedness locally in time and examine the corresponding optimal control problem numerically by means of a projected gradient method with Broyden-Fletcher-Goldfarb-Shanno (BFGS) update.     

On the Distribution of Duration of First Negative Surplus for a Discrete Time Risk Model with Random Interest Rate

In this paper, we examine further annuity-due risk model presented by Cai (Probability in the Engineering and Informational Sciences, 16(2002), 309-324). We consider the computation for the distribution of duration of first negative surplus and the algorithm is shown for calculating probability that ruin occurs and the duration of first negative surplus takes any nonnegative integers values. Numerical illustration for the main result is given.     

Necessary conditions of optimality for a class of second-order hyperbolic systems with spatially dependent controls in the coefficients

In the paper, we consider the problem of parameter optimization for a class of second-order hyperbolic systems with distributional forcing terms. After necessary preparations in Sections 1 and 3, we develop in Section 4 the necessary conditions of optimality for the system with quadratic cost function. In Section 5, we extend these results to cover a wider class of controls; we also prove the existence of suboptimal policies. An example is presented indicating possible application to power system regulation problems.This work was supported in part by the National Science and Engineering Council of Canada under Grant No. 7109.The author would like to thank Professor L. Cesari for pointing out in a private communication that there are situations like the Lavrentiev phenomenon in which an approximation analogous to that given in Theorem 5.3 is not possible.     

On the usage of refined linear models for determiningN-way classification designs which are optimal for comparing test treatments with a standard treatment

Summary In this paper we consider experimental settings in whichv test treatments are to be compared to some control or standard treatment and where heterogeneity needs to be eliminated inn-directions. Using techniques similar to those used by Kunnert (1983,Ann. Statist.,11, 247–257) concerning the determination of optimal designs under a refined linear model, some methods are given for constructingn-way classification designs which areA- andMV-optimal for estimating elementary treatment differences involving the standard treatment fromm-way classification designs,m<n, which areA- andMV-optimal for estimating the same treatment differences. Examples are given for the casen=2 to show how the results obtained can be applied. This research was supported by NSF grant No. DMS-8401943.