线性等式约束多目标规划的一个降维算法

本文提出具有线性等式约束多目标规划问题的一个降维算法．当目标函数全是二次或线性但至少有一个二次型时，用线性加权法转化原问题为单目标二次规划，再用降维方法转化为求解一个线性方程组．若目标函数非上述情形，首先用线性加权法将原问题转化为具有线性等式约束的非线性规划，然后，对这一非线性规划的目标函数二次逼近，构成线性等式约束二次规划序列，用降维法求解，直到满足精度要求为止．     

分段线性规划算法的一个注记

求解分段线性规划问题inf S(x) s.t.Ax≤b 0≤x≤(?) (1)其中(?)=((?)_1,(?)_2,…,(?)_n)及 b=(b_1,b_2,…,b_m)~T 是已知向量,A 是已知的(m,n)矩阵,元素为 α_(ij)。目标函数 s(x)是分段线性函数。即对[0,(?)_j)(j=1,2,…,n)存在分划0=x_j~(0)相似文献   

利用线性规划思想解题

解决线性规划问题的数学思想 ,从本质上谈就是数形结合 .当约束条件或目标函数不是线性思题 ,而其几何意义明显 ,这时仍可利用线性规划的思想来解决问题 ,使解题思路拓宽 ,思维拓展 ,从而提高学生的解题能力 .1　函数问题转化为规划问题例 1　已知二次函数f(x) =ax2 +bx + 1 (a ,b∈R ,a >0 ) ,设方程f(x) =x的两实根为x1 和 图 1　例 1图x2 ,如果x1 <2 1 .证　设g(x) =f(x)-x =ax2 + (b - 1 )x + 1由题意 ,利用线性规划思想解题@商俊宇$临沂市罗庄区第一中学!山东276017…     

求解一类广义线性规划的分裂算法

1　引　　言我们知道,描述常义线性规划问题的数学模型为:mincTxs.tAx=bx≥0　　在经济问题中,线性规划中的向量c往往表示为价格,而在许多实际规划问题中价格向量c往往会在一定范围内扰动.这时,我们可以考虑这样一类广义线性规划问题:minx{maxy∈YyTx}s.tAx=b　x∈X(1)其中,A∈Rm×n,b∈Rm,X={x∈Rn|x≥0},Y是Rn中的一个凸闭子集.有关广义线性规划问题的求解,何在文献[1]中作过一些讨论.我们通过对线性约束Ax=b引入乘子可得到广义线性规划问题(1)定义在X×Y×Rm上的Lagrange函数为:L(x,y,η)=yTx-ηT(Ax-b)(2)　　如果x*是(1)式的…     

广义几何规划的全局优化算法

对许多工程设计中常用的广义几何规划问题(GGP)提出一种确定性全局优化算法,该算法利用目标和约束函数的线性下界估计,建立GGP的松弛线性规划(RLP),从而将原来非凸问题(GGP)的求解过程转化为求解一系列线性规划问题(RLP).通过可行域的连续细分以及一系列线性规划的解,提出的分枝定界算法收敛到GGP的全局最优解,且数值例子表明了算法的可行性.     

非线性的规划问题

我们知道,线性规划研究的是线性约束条件下线性目标函数的最值,那么类似的会有非线性的规划问题,主要是下面三类问题:(1)非线性约束条件下求线性目标函数的最值;(2)线性约束条件下求非线性目标函数的最值;     

应用模糊目标规划方法求解多目标线性分式规划问题

针对多目标分式线性规划问题,提出利用上(下)界表示目标期望水平及允许上(下)限,且利用一阶泰勒公式逼近隶属函数,将多目标分式规划转化为线性规划问题,并用单纯形法求解,通过实验算例说明了所提出的方法的有效性.     

(p,r)-不变凸函数规划问题的鞍点定理

本文首先介绍了一个广义Lagrange向量函数L(x,u),并利用一类新的广义 凸函数:(p,r)——不变凸函数讨论了多目标分式规划问题的鞍点最优性条件．     

分数布朗运动驱动的一类随机微分方程的弱解问题

本文,我们研究如下分数布朗运动驱动的一类随机微分方程的弱解问题Xt=x+BHt+∫t0b(s,Xs)ds,其中BH={BHt,0≤t≤T}是Hurst指数为H∈(0,1/2)∪(1/2,1)的分数布朗运动,b是Borel可测函数且满足线性增长条件|b(t,x)|≤(1+|x|)f(t),其中x∈R且0＜t＜T,f是非负...     

在直线与二次曲线围成的可行域上求目标函数最值

在线性规划中,可行域都是直线围成的平面区域,我们能求出目标函数的最值,当可行域由直线与二次曲线围成时,如何求目标函数的最值呢?现在就让我们一起来学习探讨.例1已知x,y满足(x-2)2 y2-1≤0,x-3y≤0,求x y3的最大值和最小值.分析x y3可看作动点M(x,y)与定点B(-3,0)所在直线的     

Solving Quadratically Constrained Least Squares Problems Using a Differential-Geometric Approach

A quadratically constrained linear least squares problem is usually solved using a Lagrange multiplier for the constraint and then solving iteratively a nonlinear secular equation for the optimal Lagrange multiplier. It is well-known that, due to the closeness to a pole for the secular equation, standard methods for solving the secular equation can be slow, and sometimes it is not easy to select a good starting value for the iteration. The problem can be reformulated as that of minimizing the residual of the least squares problem on the unit sphere. Using a differential-geometric approach we formulate Newton's method on the sphere, and thereby avoid the difficulties associated with the Lagrange multiplier formulation. This Newton method on the sphere can be implemented efficiently, and since it is easy to find a good starting value for the iteration, and the convergence is often quite fast, it has a clear advantage over the Lagrange multiplier method. A numerical example is given.     

解并行处理机最优映射问题的遗传算法

该文给出了一种用于多处理机系统中实现并行计算的最优映射问题的遗传算法,它对于在固定结构的并行系统中充分利用计算资源,提高计算效率具有实用价值,实践表明,采用遗传算法是解决任务最优映射问题的有效的方法．     

Fast heuristic for constrained homogenous T-shape cutting patterns

Homogenous T-shape (HTS) cutting patterns are welcomed when the two-phase process is used to produce rectangular pieces from the stock plate, where the plate is cut into homogenous strips at the first phase, and the strips are divided into pieces at the second phase. A heuristic is presented for generating constrained HTS patterns, where the objective is to maximize the pattern value that is equal to the total value of the included pieces, observing the upper bound constraint on the frequency of each piece type. The heuristic is based on dynamic programming and branch-and-bound techniques. It can yield solutions close to optimal with short computation time. By providing good initial solutions, the heuristic can greatly improve the time efficiency of an existing exact branch-and-bound algorithm.     

The consistent Shapley value for hyperplane games

A new value is defined for n-person hyperplane games, i.e., non-sidepayment cooperative games, such that for each coalition, the Pareto optimal set is linear. This is a generalization of the Shapley value for side-payment games. It is shown that this value is consistent in the sense that the payoff in a given game is related to payoffs in reduced games (obtained by excluding some players) in such a way that corrections demanded by coalitions of a fixed size are cancelled out. Moreover, this is the only consistent value which satisfies Pareto optimality (for the grand coalition), symmetry and covariancy with respect to utility changes of scales. It can be reached by players who start from an arbitrary Pareto optimal payoff vector and make successive adjustments.     

在折现率大于零的情况下,具有完成时间和残值不确定性的R&D项目的投资策略

利用随机停时理论 ,考虑 R&D项目的连续投资策略 .在折现率大于零的情况下 ,给出了具有建设期和残值的不确定性的 R&D投资模型、放弃 R&D项目投资的临界值和最优决策规则 ,并讨论参数对临界值的影响 .也进一步验证了随机停时理论和实物期权理论在投资决策分析中的一致性 .     

Optimal insurance in the presence of insurer’s loss limit

In this paper we consider the optimal insurance problem when the insurer has a loss limit constraint. Under the assumptions that the insurance price depends only on the policy’s actuarial value, and the insured seeks to maximize the expected utility of his terminal wealth, we show that coverage above a deductible up to a cap is the optimal contract, and the relaxation of insurer’s loss limit will increase the insured’s expected utility.When the insurance price is given by the expected value principle, we show that a positive loading factor is a sufficient and necessary condition for the deductible to be positive. Moreover, with the expected value principle, we show that the optimal deductible derived in our model is not greater (lower) than that derived in Arrow’s model if the insured’s preference displays increasing (decreasing) absolute risk aversion. Therefore, when the insured has an IARA (DARA) utility function, compared to Arrow model, the insurance policy derived in our model provides more (less) coverage for small losses, and less coverage for large losses.Furthermore, we prove that the optimal insurance derived in our model is an inferior (normal) good for the insured with a DARA (IARA) utility function, consistent with the finding in the previous literature. Being inferior, the insurance can also be a Giffen good. Under the assumption that the insured’s initial wealth is greater than a certain level, we show that the insurance is not a Giffen good if the coefficient of the insured’s relative risk aversion is lower than 1.     

Variational Calculus and Approximate Solution of Optimal Control Problems

Variational calculus is a differential process whereby Taylor series expansions can be developed on a term-by-term basis. Therefore, it can be used to obtain the equations which must be solved for the various-order terms arising from the application of regular perturbation theory to problems involving a small parameter. Variational calculus is summarized and applied to the approximate analytical solution of the optimal control problem. First, the various-order equations are obtained directly for a particular problem. Then, assuming that the zeroth-order solution is almost good enough, the equations for the first-order correction are obtained for the general optimal control problem and applied to the particular problem. The first-order solution is the same as the neighboring extremal for the given value of the parameter.     

OPTIMAL INVESTMENT IN THE PROTECTION OF A VULNERABLE BIOLOGICAL RESOURCE

It is assumed that the probability of destruction of a biological asset by natural hazards can be reduced through investment in protection. Specifically a model, in which the hazard rate depends on both the age of the asset and the accumulated invested protection capital, is assumed. The protection capital depreciates through time and its effectiveness in reducing the hazard rate is subject to diminishing returns. It is shown how the investment schedule to maximize the expected net present value of the asset can be determined using the methods of deterministic optimal control, with the survival probability regarded as a state variable. The optimal investment pattern involves “bang-bang-singular” control. A numerical scheme for determining jointly the optimal investment policy and the optimal harvest (or replacement) age is outlined and a numerical example involving forest fire protection is given.     

A Note on the Suboptimality of Path-Dependent Pay-Offs in Lévy Markets

Abstract

Cox and Leland used techniques from the field of stochastic control theory to show that, in the particular case of a Brownian motion for the asset log-returns, risk-averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent pay-offs. In this note we provide a novel and simple proof for the Cox and Leland result and we will extend it to general Lévy markets where pricing is based on the Esscher transform (exponential tilting). It is also shown that, in these markets, optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant. Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view.     

Finding maxmin allocations in cooperative and competitive fair division

We define a subgradient algorithm to compute the maxmin value of a completely divisible good in both competitive and cooperative strategic contexts. The algorithm relies on the construction of upper and lower bounds for the optimal value which are based on the convexity properties of the range of utility vectors associated to all possible divisions of the good. The upper bound always converges to the optimal value. Moreover, if two additional hypotheses hold: that the preferences of the players are mutually absolutely continuous, and that there always exists relative disagreement among the players, then also the lower bound converges, and the algorithm finds an approximately optimal allocation.