Optimality Conditions and Stability Analysis via the Mordukhovich Subdifferential

This article shows that finite-dimensional multiplier rules, which are based on the limiting subdifferential, can be proved by Ekeland's variational principle and some basic calculus tools of the generalized differentiation theory introduced by B. S. Mordukhovich. Consequences of a limiting constraint qualification, which yields the normal form of the multiplier rules, stability and calmness of optimization problems, are investigated in detail.     

一种新的逼近精确罚函数的罚函数及性质

针对可微非线性规划问题提出了一个新的逼近精确罚函数的罚函数形式,给出了近似逼近算法与渐进算法,并证明了近似算法所得序列若有聚点,则必为原问题最优解. 在较弱的假设条件下,证明了算法所得的极小点列有界,且其聚点均为原问题的最优解,并得到在Mangasarian-Fromovitz约束条件下,经过有限次迭代所得的极小点为可行点.     

Directed Subdifferentiable Functions and the Directed Subdifferential Without Delta-Convex Structure

We show that the directed subdifferential introduced for differences of convex (delta-convex, DC) functions by Baier and Farkhi can be constructed from the directional derivative without using any information on the delta-convex structure of the function. The new definition extends to a more general class of functions, which includes Lipschitz functions definable on o-minimal structure and quasidifferentiable functions.     

基于罚函数方法的Leach协议

为延长无线传感器网络生存时长、减少网络能量消耗,首先将自适应粒子群优化算法应用于Leach协议,获得每一轮的最优簇头集;再基于罚函数方法,对集合中处于边缘位置的感知节点以及基站附近能量较低的感知节点进行惩罚,降低其当选为簇头的概率.通过大量仿真实验表明,协议对网络中簇头节点的选取更加合理,死亡节点分布由外而内,使节点能量负载更加均衡.     

Subdifferential Properties of Quasiconvex and Pseudoconvex Functions: Unified Approach

In this paper, we are mainly concerned with the characterization of quasiconvex or pseudoconvex nondifferentiable functions and the relationship between those two concepts. In particular, we characterize the quasiconvexity and pseudoconvexity of a function by mixed properties combining properties of the function and properties of its subdifferential. We also prove that a lower semicontinuous and radially continuous function is pseudoconvex if it is quasiconvex and satisfies the following optimality condition: 0f(x)f has a global minimum at x. The results are proved using the abstract subdifferential introduced in Ref. 1, a concept which allows one to recover almost all the subdifferentials used in nonsmooth analysis.     

一类新的罚函数与罚算法(英)

在本文中,我们提出了带不等式约束的非线性规划问题的一类新的罚函数,它的一个子类可以光滑逼近$l_1$罚函数. 基于此类新的罚函数我们给出了一种罚算法,这个算法的特点是每次迭代求出罚函数的全局精确解或非精确解. 在很弱的条件下算法总是可行的. 我们在不需要任何约束规范的情况下,证明了算法的全局收敛性. 最后给出了数值实验.     

A Branch-and-Bound Method for Sequencing Problems with Linear and Exponential Penalty Functions

Journal of the Operational Research Society - By utilising a known result for the single machine case, a branch-and-bound method is derived for the solution of the n-job, m-machine sequencing...     

New Weighted Estimates for the Disc Multiplier on Radial Functions

Journal of Fourier Analysis and Applications - We prove a weighted estimate for the disc multiplier, acting on radial functions, at the extreme points $$p_{-}=frac{2n}{n+1}$$ , extending the...     

拉格朗日乘数法的几何理解

结合目标函数等值线族与条件曲线的图像,从几何上认识拉格朗日乘数法,理解拉格朗日乘数法在解决条件极值问题过程中的必要非充分性.     

Alternative Representations of the Normal Cone to the Domain of Supremum Functions and Subdifferential Calculus

Set-Valued and Variational Analysis - The first part of the paper provides new characterizations of the normal cone to the effective domain of the supremum of an arbitrary family of convex...     

基于Lagrange乘子法的一种二阶椭圆问题混合元格式

本文利用Lagrange乘子法的思想,修改了传统的混合变分形式,将二阶椭圆问题转化为与其等价的新的变分形工,给出了针对该新形式进行离散求解的一种混合元格式,与现在已知格式相比,用较少的自由度获得了较高的逼近阶。     

Extended Lagrange and Penalty Functions in Optimization

We consider nonlinear Lagrange and penalty functions for optimization problems with a single constraint. The convolution of the objective function and the constraint is accomplished by an increasing positively homogeneous of the first degree function. We study necessary and also sufficient conditions for the validity of the zero duality gap property for both Lagrange and penalty functions and for the exact penalization. We also study the so-called regular weak separation functions.     

Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions

Journal of Optimization Theory and Applications - This paper mainly studies the quadratic growth and the strong metric subregularity of the subdifferential of a function that can be represented as...     

A Smooth Embedding Domain Method Based On the Penalty Approach

It is well known that convergence of the fictitious domain formulation with boundary Lagrange multipliers is slow due to the lower global regularity of its solution. This article presents a smoothed variant of this approach which is based on a formulation in the form of a state constraint optimal control problem. The convergence rate is increased as seen from a model example.     

巧用Lagrange乘数法求一类多元对称函数的条件最值

巧用Lagrange乘数法,将一类多元对称函数的条件最值转化为一元函数的无条件最值,避免了具体求复杂而困难的驻点方程组的解,使问题化难为易.     

The P-version Penalty Finite Element Method

A p-version penalty finite element method is used to solve themodel problem –u=f in , u=g on . Error estimates are derivedin H¹-norm. The p-version penalty method with extrapolationyields an approximate solution which converges at the optimalrate. Numerical results show the effectiveness of the p-versionpenalty method with extrapolation.     

计数集团检查的抽查特征函数

本文给出计数型集团检查一次、二次抽样方案的抽查特征函数及其算法, 并且通过与近似算法的比较和计算机抽样检查模拟, 验证了该方法的正确性, 并对该抽查特征函数性质和应用作了初步讨论.     

具有两类索赔相关风险过程的罚金折现函数

考虑两类索赔相关风险过程.两类索赔计数过程分别为独立的Poisson和广义Erlang(2)过程.将该过程转换为两类独立索赔风险过程,得到了该过程的罚金折现函数满足的积分微分方程及该函数的拉普拉斯变换的表达式,且当索赔额服从指数分布时,给出了罚金折现函数及破产概率的表达式.     

Stochastic Networks: Admission and Routing Using Penalty Functions

We propose an admission and routing control policy for a network of service facilities in a stochastic setting in order to maximize a long run average reward. Queueing and reneging before entering the network is allowed; we introduce orbiting as an approximation to the queueing. Once a customer has entered the network, it incurs no more waiting. Our control policy is easy to implement and we prove that it performs well in steady state as long as the capacity request sizes are relatively small compared to the capacity of the service facilities. The policy is a target tracking policy: a linear program provides a target operating point and an exponential penalty function is used to translate the optimal deterministic point into a feasible admission and routing policy. This translation essentially transforms the admission and routing control problem into a problem of load balancing via the construction of fictitious systems. Simulation studies are included to illustrate that our policy also performs well when request sizes are moderate or large with respect to the capacity.     

用罚函数求解线性双层规划的全局优化方法

用罚函数法将线性双层规划转化为带罚函数子项的双线性规划问题，由于其全局最优解可在约束域的极点上找到，利用对偶理论给出了一种求解该双线性规划的方法，并证明当罚因子大于某一正数时，双线性规划的解就是原线性双层规划的全局最优解。