摘抄自:  https://en.wikipedia.org/wiki/Rearrangement_inequality#Proof In mathematics, the rearrangement inequality[1] states that {\displaystyle x_{n}y_{1}+\cdots +x_{1}y_{n}\leq x_{\sigma (1)}y_{1}+\cdots +x_{\sigma (n)}y_{n}\leq x_{1}y_{1}+\cdots +x_{…

来源:这里 Bất Đẳng Thức Luôn Có Một Sức Cuốn Hút Kinh Khủng, Một Số tài Liệu và Sách Bổ ích Cho Việc Học Tập. 1. An Introduction to Inequalities [E. Beckenbach, R. Bellman] Book title: An Introduction to Inequalities.Authors: Edwin Beckenbach, Richard Be…

题目 题目:Lunar New Year and Number Division 题目大意:给定一个数字序列,可以任意分组(可调整顺序),但每组至少两个,求每组内数字和的平方的最小值 思路 首先,易证两两分组是最好的. 其次,我们假设将序列${a_i}$分成序列${b_i}$和${c_i}$,所以 $$sum=\frac{1}{2}\sum_{i=1}^{n}(b_i+c_i)^2$$ 我们不关心这部分(因为不管怎么划分,这部分值都不会变): $$\frac{1}{2}\sum_{i=1}^{n…

http://acm.hdu.edu.cn/showproblem.php?pid=4710 Balls Rearrangement Time Limit: 6000/3000 MS (Java/Others)    Memory Limit: 32768/32768 K (Java/Others) Total Submission(s): 735    Accepted Submission(s): 305 Problem Description Bob has N balls and A b…

ArcSoft's Office Rearrangement Time Limit: 2000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)Total Submission(s): 3    Accepted Submission(s): 2 Problem Description ArcSoft, Inc. is a leading global professional computer photogra…

Balls Rearrangement Time Limit: 9000/3000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others) Total Submission(s): 1661    Accepted Submission(s): 627 Problem Description Bob has N balls and A boxes. He numbers the balls from 0 to N-1, and…

Problem Description Bob has N balls and A boxes. He numbers the balls from 0 to N-1, and numbers the boxes from 0 to A-1. To find the balls easily, he puts the ball numbered x into the box numbered a if x = a mod A.   Some day Bob buys B new boxes, a…

Balls Rearrangement Time Limit: 9000/3000 MS (Java/Others) Memory Limit: 65535/32768 K (Java/Others) Total Submission(s): 1682 Accepted Submission(s): 634 Problem Description Bob has N balls and A boxes. He numbers the balls from 0 to N-1, and number…

Balls Rearrangement Time Limit: 9000/3000 MS (Java/Others)    Memory Limit: 65535/32768 K (Java/Others) Total Submission(s): 322    Accepted Submission(s): 114 Problem Description Bob has N balls and A boxes. He numbers the balls from 0 to N-1, and n…

MM bound 与 Jensen's inequality 简森不等式 在使用最大似然估计方法求解模型最优解的时候,如果使用梯度下降(GD or SGD)或者梯度上升(GA or SGA),可能收敛的很慢. 这时,可以使用 MM bound + Jensen's inequality 相结合的方法,先用MM,然后用 Jensen's inequality,可能能得到一个最大值解.使用这个最大值解来更新参数就好了. 1.先使用 MM bound, 2.使用两个 Jensen 不等式:…