This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network...This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.展开更多
This paper presents an efficient pattern matching algorithm (FSW). FSW improves the searching process for a pattern in a text. It scans the text with the help of four sliding windows. The windows are equal to the leng...This paper presents an efficient pattern matching algorithm (FSW). FSW improves the searching process for a pattern in a text. It scans the text with the help of four sliding windows. The windows are equal to the length of the pattern, allowing multiple alignments in the searching process. The text is divided into two parts;each part is scanned from both sides simultaneously using two sliding windows. The four windows slide in parallel in both parts of the text. The comparisons done between the text and the pattern are done from both of the pattern sides in parallel. The conducted experiments show that FSW achieves the best overall results in the number of attempts and the number of character comparisons compared to the pattern matching algorithms: Two Sliding Windows (TSW), Enhanced Two Sliding Windows algorithm (ETSW) and Berry-Ravindran algorithm (BR). The best time case is calculated and found to be??while the average case time complexity is??.展开更多
This paper modifies the Frank-Wolfe's algorithm. Under weaker conditions it proves that the modified algorithm is convergent, and specially under the assumption of convexity of the objective function that without...This paper modifies the Frank-Wolfe's algorithm. Under weaker conditions it proves that the modified algorithm is convergent, and specially under the assumption of convexity of the objective function that without assuming {x￣k} is bounded.展开更多
建立了一套基于计算流体力学（CFD）/FW-H_pds方程（Ffowcs Williams-Hawkings equations with penetrable data surface）的气动噪声预估技术和组合优化算法的低噪声旋翼桨尖平面外形设计方法。首先,采用积分形式的可压雷诺平均Navier-...建立了一套基于计算流体力学（CFD）/FW-H_pds方程（Ffowcs Williams-Hawkings equations with penetrable data surface）的气动噪声预估技术和组合优化算法的低噪声旋翼桨尖平面外形设计方法。首先,采用积分形式的可压雷诺平均Navier-Stokes（RANS）方程作为旋翼流场求解控制方程,围绕旋翼流场的网格采用嵌套网格方法生成。在优化过程中,桨叶网格生成采用提出的高效参数化的网格自动生成方法。在建立的CFD方法求解基础上,采用基于可穿透旋转积分面的鲁棒性较好的FW-H_pds方程来求解旋翼高速脉冲（HSI）噪声。然后,以降低旋翼HSI噪声为目标,以旋翼悬停气动性能为约束,提出具备前掠-后掠-尖削等组合特征的桨尖外形方案并进行优化分析。将基于拉丁超立方（LHS）方法和径向基函数（RBF）的代理模型方法耦合到遗传算法过程中,建立了一种高效的组合优化算法。在当前的计算状态下,优化后的桨尖外形的负压峰值相比于矩形桨叶降低了58.4%,优化后的桨叶有效地减弱了旋翼桨尖区域的跨声速“离域化”现象,因此可以降低旋翼HSI噪声特性,同时可以减弱旋翼桨尖涡强度达30%,旋翼悬停性能提高了2%~3%。展开更多
基金supported in part by the National Key R&D Program of China(2021YFB1714800)the National Natural Science Foundation of China(62222303,62073035,62173034,61925303,62088101,61873033)+1 种基金the CAAI-Huawei MindSpore Open Fundthe Chongqing Natural Science Foundation(2021ZX4100027)。
文摘This paper considers distributed stochastic optimization,in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network.Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent.However,projecting a point onto a feasible set is often expensive.The Frank-Wolfe(FW)method has well-documented merits in handling convex constraints,but existing stochastic FW algorithms are basically developed for centralized settings.In this context,the present work puts forth a distributed stochastic Frank-Wolfe solver,by judiciously combining Nesterov's momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks.It is shown that the convergence rate of the proposed algorithm is O(k^(-1/2))for convex optimization,and O(1/log_(2)(k))for nonconvex optimization.The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.
文摘This paper presents an efficient pattern matching algorithm (FSW). FSW improves the searching process for a pattern in a text. It scans the text with the help of four sliding windows. The windows are equal to the length of the pattern, allowing multiple alignments in the searching process. The text is divided into two parts;each part is scanned from both sides simultaneously using two sliding windows. The four windows slide in parallel in both parts of the text. The comparisons done between the text and the pattern are done from both of the pattern sides in parallel. The conducted experiments show that FSW achieves the best overall results in the number of attempts and the number of character comparisons compared to the pattern matching algorithms: Two Sliding Windows (TSW), Enhanced Two Sliding Windows algorithm (ETSW) and Berry-Ravindran algorithm (BR). The best time case is calculated and found to be??while the average case time complexity is??.
文摘This paper modifies the Frank-Wolfe's algorithm. Under weaker conditions it proves that the modified algorithm is convergent, and specially under the assumption of convexity of the objective function that without assuming {x￣k} is bounded.
文摘建立了一套基于计算流体力学（CFD）/FW-H_pds方程（Ffowcs Williams-Hawkings equations with penetrable data surface）的气动噪声预估技术和组合优化算法的低噪声旋翼桨尖平面外形设计方法。首先,采用积分形式的可压雷诺平均Navier-Stokes（RANS）方程作为旋翼流场求解控制方程,围绕旋翼流场的网格采用嵌套网格方法生成。在优化过程中,桨叶网格生成采用提出的高效参数化的网格自动生成方法。在建立的CFD方法求解基础上,采用基于可穿透旋转积分面的鲁棒性较好的FW-H_pds方程来求解旋翼高速脉冲（HSI）噪声。然后,以降低旋翼HSI噪声为目标,以旋翼悬停气动性能为约束,提出具备前掠-后掠-尖削等组合特征的桨尖外形方案并进行优化分析。将基于拉丁超立方（LHS）方法和径向基函数（RBF）的代理模型方法耦合到遗传算法过程中,建立了一种高效的组合优化算法。在当前的计算状态下,优化后的桨尖外形的负压峰值相比于矩形桨叶降低了58.4%,优化后的桨叶有效地减弱了旋翼桨尖区域的跨声速“离域化”现象,因此可以降低旋翼HSI噪声特性,同时可以减弱旋翼桨尖涡强度达30%,旋翼悬停性能提高了2%~3%。
