differentiable
Examples
- This paper discusses a variation equation problem in a class of singular stochastic control with stopping time , gives its solution under two different conditions , which is a one order continuous differentiable and concave function , and gives the exact form
摘要讨论了一类带停时的奇异型随机控制问题中的一个变分方程问题,并且在两种不同的情况下给出了该变分方程的解,即为一阶连续可导凹函数,并在两种情况下给出了此函数的具体形式。 - Because ga possesses the traits of can global random search , the robustness is strong , been use briefly and broadly , it didn ’ t use path search , and use probability search , didn ’ t care inherence rule of problem itself , can search the global optimum points effectively and rapidly in great vector space of complicated , many peak values , cannot differentiable . so it can offset the shortages of nn study algorithm , can reduce the possibility that the minimum value get into local greatly , the speed of convergence can improve , interpolation time shorten greatly , the quantity of training reduce
因为遗传算法具有全局随机搜索能力,鲁棒性强、使用简单和广泛的特点,它不采用路径搜索,而采用概率搜索,不用关心问题本身的内在规律,能够在复杂的、多峰值的、不可微的大矢量空间中迅速有效地寻找到全局最优解,所以可以弥补神经网络学习算法的不足,使陷入局部最小值的可能性大大减少,使得收敛速度提高,训练量减小。 - We extend this result which is similar to ones of hirsch [ 1l ] and jiang [ 2 ] for 3 - dimensional cooperative system . furthermore , in the paper we discusse the cone of km , and obtain the similar result : theorem b : let f be a continuously differentiable cooperative vector field on d , suppose the following conditions hold : ( a ) d is pm - convex ; ( b ) every forward semi - orbit has compact closure in d ; ( c ) there is not more than one equilibrium p , then there is a unique equilibrium p and it is globally asymptotically stable
此外,本文还将在k _ m锥下讨论此问题,并得到平行的结果:定理b :设f是d上一个连续可微的合作向量场,假设如下条件成立: ( a ) d是p _ m凸的; ( b ) d中的每一个正半轨道有紧闭包; ( c )至多有一个平衡点p ,则一定存在唯一的平衡点p ,并且是全局渐近稳定的。 - Let f ( x ) and f ( x ) stand for the generalized gradients proposed by clarke and xu yihong respectively . three of generalized gradients are compared and the inclusion relation between them is so the set of the generalized gradient defined in this paper is smaller ; they coincide when / is a convex function or f is differentiable
文中对三类广义梯度进行比较,若以和分别表示clarke和徐义红定义的广义梯度,三者之间的包含关系为即本文定义的广义梯度集合较小;而当f为凸函数或f可微时,三者统一。 - Having developed for half an century , the conventional optimization algorithms which are based on the operational research theory and some mathematical programming tools come into mature . such algorithms have been widely used in many fields due to their high efficiency and robustness . however , they usually require the optimized functions to be continuous even high order differentiable
这些在运筹学( operationalresearch )和数学规划工具( mathematicalprogramming )基础上形成的最优化算法,具有理论完备、算法效率高、稳定性好等优点,因而在许多需要进行优化计算的场合被广泛的使用。 - Furthermore , when replacing the entropy function by a general separate multiplier function , we develop a new regularization approach , referred to as lagrangian regularization approach . this approach does not only provide a unified smoothing technique for the non - differentiable m ( x ) and but also offers a unified framework for constructing penalty functions , whereby building a bridge between the penalty functions and the classical lagrangian
该方法不仅提供了统一光滑不可微函数m ( x )和( ? | r _ - ~ m )的办法,而且还给出了一种构造罚函数的统一框架,由此将罚函数与经典拉格朗日函数从对偶空间的角度联系在一起。 - To circumvent the non - differentiable difficulty caused by the positive homogeneously function that is involved in an equivalent unconstrained formulation for general inequality constrained optimization problems , we turn to the classical lagrangian function and redefine m ( x ) by a conic optimization problem with the lagrangian as the objective function
为了克服不可微正齐次函数( ? | r _ - ~ m )给约束优化问题的等价无约束形式求解带来的困难,我们将其目标函数m ( x )重新用一个以经典拉格朗日函数为目标的锥优化问题来表示。 - Nonlinear operator theorem is now a focus in nonlinear theorem . the study of the ergodic theory for semitopologocal semigroups of nonlinear operators began in the middle of 1970 ' s . it got great development because it was widely used in many problems , such as the numerical solution of differentiable equation , the existence theory of positive solution , contral theory and optimization
非线性算子理论是非线性理论中的热门话题,它的研究始于上世纪七十年代中期,由于它被广泛的应用于微分方程的数值解、正解的存在性理论、控制论以及最优化等问题中,因而得到了很大的发展。
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