最大化向量的列乘法答案

【问题标题】：Maximize column-wise multiplication of vector最大化向量的列乘法
【发布时间】：2019-05-06 09:56:39
【问题描述】：

给定矩阵M

M <- structure(c(0.0700078597292304, -0.0136474068276584, 0.328056303784251, 
-0.459178164601326, -0.586918574757874, 0.791669885627925, -0.877064344473183, 
0.882802148349583, 0.421708580106497, -0.110332333017141, -0.287893873639405, 
0.00899101700633764, -0.705056414008141, -0.897502972278744, 
0.0145046846009791, -0.409322344232351, 0.622156938537955, 0.941861041355878, 
0.622148288879544, 0.741163543891162, 0.695223031565547, 0.514508185908198, 
-0.297026146668941, -0.930878807790577, 0.72842172626406, 0.899442498106509, 
-0.0246643857099116, 0.993599037639797, 0.150956830941141, 0.341335460077971
), .Dim = c(10L, 3L))

             # [,1]         [,2]        [,3]
 # [1,]  0.07000786 -0.287893874  0.69522303
 # [2,] -0.01364741  0.008991017  0.51450819
 # [3,]  0.32805630 -0.705056414 -0.29702615
 # [4,] -0.45917816 -0.897502972 -0.93087881
 # [5,] -0.58691857  0.014504685  0.72842173
 # [6,]  0.79166989 -0.409322344  0.89944250
 # [7,] -0.87706434  0.622156939 -0.02466439
 # [8,]  0.88280215  0.941861041  0.99359904
 # [9,]  0.42170858  0.622148289  0.15095683
# [10,] -0.11033233  0.741163544  0.34133546

如何找到一个向量w（单位区间内w的每个元素）使w和M的列乘法之和最大化（混合sum(M %*% w)）？

【问题讨论】：

您对“逐列乘法之和”的理解到底是什么？ sum(M %*% w)?
也许：fn <- function(w) sum(M %*% w); optim(rep(0, 3), fn, lower = 0, upper = 1, method = "L-BFGS-B", control = list(fnscale = -1))
这应该回答我的澄清请求吗？因为事实并非如此。

标签： r matrix

【解决方案1】：

只需定义您的目标函数：

fn <- function(w) sum(M %*% w)

然后优化：

optim(rep(0, 3), fn, lower = 0, upper = 1, method = "L-BFGS-B", control = list(fnscale = -1))
#$par
#[1] 1 1 1
#
#$value
#[1] 4.169071
#
#$counts
#function gradient 
#       4        4 
#
#$convergence
#[1] 0
#
#$message
#[1] "CONVERGENCE: NORM OF PROJECTED GRADIENT <= PGTOL"

【讨论】：