在 R 中使用 L-BFGS-B 方法优化时的非有限有限差分误差

【问题标题】：Non-finite finite difference error when using optim with L-BFGS-B method in R在 R 中使用 L-BFGS-B 方法优化时的非有限有限差分误差
【发布时间】：2021-12-18 01:57:55
【问题描述】：

我正在尝试使用我的对数似然函数获得五个参数（1 pi，范围在 0 和 1 之间的比例，4 个 beta 是指数下降率）的置信区间。我的数据包括疫苗接种后的时间间隔、分类为 1 和 0 的免疫状态以及过去的疫苗接种历史和个体狗的所有权状态。我的数据如下

data4mle <- 
  structure(
    list(
      Interval_18 = c(35, 123, 13, 140, 8, 115, 16, 
                      131, 132, 8, 13, 146, 44, 15, 138, 3, 143, 149, 12, 153, 17, 
                      154, 14, 8, 123, 16, 17, 154, 8, 135, 10, 133, 18, 8, 123, 10, 
                      133, 16, 163, 10, 150, 10, 3, 8, 8, 139, 22, 9, 122, 1, 130, 
                      16, 140, 16, 140, 20, 142, 42, 122, 16, 8, 126, 8, 8, 139, 20, 
                      122, 14, 8, 122, 146, 6, 20, 9, 6, 13, 13, 115, 12, 131, 12, 
                      12, 23, 116, 6, 102, 13, 137, 6, 107, 12, 14, 115, 18, 123, 155, 
                      158, 163, 35, 155, 16, 163, 16, 140, 44, 128, 9, 21, 36, 46, 
                      153, 27, 147, 47, 131, 8, 146, 12, 17, 9, 16, 155, 9, 10, 148, 
                      32, 148, 25, 15, 138, 46, 158, 121, 8, 131, 8, 8, 118, 31, 154, 
                      32, 144, 15, 8, 16, 8, 101, 15, 144, 12, 20, 10, 15, 142, 13, 
                      69, 28, 168, 15, 12, 24, 13, 142, 12, 115, 13, 131, 166, 13, 
                      118, 12, 32, 6, 36, 164, 16, 135, 20, 46, 19, 137, 11, 150, 6, 
                      107, 10, 148, 13, 118, 19, 164, 10, 16, 127, 19, 161, 156, 14, 
                      16, 145, 1, 143, 16, 5, 144, 158, 33, 19, 6, 6, 115, 16, 138, 
                      32, 13, 18, 13, 11, 158, 10, 151, 16, 16, 69, 17, 166, 26, 158, 
                      11, 11, 26, 16, 173, 16, 32, 155, 12, 16, 149, 16, 149, 16, 163, 
                      153, 57, 13, 128, 12, 113, 19, 144, 21, 35, 30, 30, 157, 108, 
                      14, 16, 33, 23, 149, 14, 14, 8, 18, 164, 115, 19, 11, 151, 19, 
                      144, 21, 13, 142, 54, 150, 16, 163, 22, 13, 11, 155, 155, 16, 
                      150, 16, 16, 57, 19, 17, 135, 12, 11, 12, 145, 11, 11, 170, 18, 
                      164, 10, 16, 12, 11, 155, 27, 11, 24, 16, 135, 47, 12, 17, 149, 
                      11, 12, 18, 137, 10, 131, 11, 151, 12, 131, 11, 158, 57, 12, 
                      5, 27, 23, 16, 24, 149, 29, 150, 12, 16, 157, 16, 10, 152, 16, 
                      10, 149, 23, 11, 30, 16, 141, 27, 147, 11, 151, 16, 157, 71, 
                      172, 32, 151, 11, 151, 10, 131, 27, 147, 22, 23, 20, 139, 10, 
                      131, 12, 145, 16, 149, 10, 135, 145, 13, 135, 16, 149, 30, 150, 
                      16, 163, 141, 51, 131, 16, 25, 16, 140, 32, 144, 41, 129, 14, 
                      8, 123, 16, 149, 101, 14, 94, 10, 139, 8, 10, 130, 96, 8, 24, 
                      144, 8, 8, 129, 20, 129, 10, 131, 8, 9, 131, 8, 127, 10, 130, 
                      22, 142, 8, 127, 13, 127, 10, 131, 10, 131, 24, 166, 8, 129, 
                      10, 131, 9, 20, 146, 8, 127, 10, 134, 10, 131, 10, 132, 10, 15, 
                      15, 20, 142, 8, 127, 11, 9, 11, 170, 10, 131, 20, 129, 144, 10, 
                      130, 10, 130, 8, 127, 10, 131, 8, 8, 130, 10, 14, 128, 10, 148, 
                      13, 127, 10, 131, 8, 127, 9, 125, 14, 129, 13, 13, 129, 27, 147, 
                      9, 131, 8, 130, 14, 128, 1, 105, 1, 105, 9, 13, 137, 8, 10, 131, 
                      17, 148, 13, 127, 8, 10, 8, 10, 10, 122, 116, 14, 128, 14, 128, 
                      11, 159, 10, 131, 20, 122), 
      Immune_status = c(1, 1, 0, 0, 1, 
                        0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 
                        1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 
                        1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 0, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 
                        0, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 
                        0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 
                        1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 
                        1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 
                        1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 
                        0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 
                        1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 
                        0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 
                        1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 
                        1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 
                        1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 
                        0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 
                        1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 
                        0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 
                        1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 
                        1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 0, 
                        1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 0, 1, 1, 1, 1, 1, 
                        0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1), 
      Owned = c("No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                "Yes", "No", "No", "No", "No", "No", "Yes", "Yes", "No", "Yes", 
                "Yes", "No", "Yes", "Yes", "Yes", "Yes", "No", "No", "No", "Yes", 
                "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "No", "Yes", 
                "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "Yes", "Yes", "No", 
                "No", "No", "No", "No", "No", "Yes", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "Yes", "Yes", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "Yes", "Yes", "Yes", 
                "Yes", "No", "Yes", "Yes", "No", "No", "No", "No", "No", "No", 
                "Yes", "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "No", 
                "No", "Yes", "Yes", "No", "No", "No", "No", "No", "Yes", "No", 
                "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "Yes", "Yes", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                "Yes", "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "Yes", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "Yes", "Yes", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "Yes", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "Yes", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "Yes", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "Yes", "No", "Yes", "Yes", "No", "Yes", "Yes", 
                "No", "No", "No", "Yes", "No", "No", "No", "No", "Yes", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                "Yes", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "No", "No", "No", "Yes", "Yes", "No", "Yes", "Yes", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "Yes", "Yes", "No", "No", "No", "No", "No", "No", "Yes", "Yes", 
                "No", "No", "No", "No", "No", "No", "No", "Yes", "No", "No", 
                "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                "No", "No", "Yes", "Yes", "Yes", "Yes", "No", "No", "No", "Yes", 
                "No", "No", "No", "Yes", "Yes", "No", "No", "No", "Yes", "Yes", 
                "No", "No", "No", "No", "No", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "No", 
                "No", "No", "No", "Yes", "No", "No", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", 
                "No", "No"), 
      Not_vacc_not_revacc_before_R3 = c("No", "No", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "No", "No", "No", "No", 
                                        "No", "No", "Yes", "Yes", "No", "Yes", "Yes", "No", "No", "Yes", 
                                        "No", "No", "No", "Yes", "Yes", "No", "Yes", "Yes", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                                        "No", "Yes", "Yes", "No", "Yes", "No", "No", "No", "No", "No", 
                                        "Yes", "Yes", "Yes", "Yes", "No", "No", "No", "No", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "Yes", "No", "Yes", "Yes", 
                                        "No", "Yes", "No", "No", "No", "Yes", "Yes", "No", "No", "Yes", 
                                        "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "No", "No", 
                                        "No", "No", "No", "Yes", "Yes", "No", "No", "No", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "Yes", "Yes", "No", "No", 
                                        "Yes", "Yes", "No", "Yes", "No", "No", "No", "Yes", "Yes", "Yes", 
                                        "No", "No", "No", "No", "Yes", "No", "No", "Yes", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                                        "No", "No", "No", "No", "No", "No", "No", "No", "No", "Yes", 
                                        "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "Yes", "Yes", 
                                        "No", "No", "Yes", "Yes", "No", "No", "No", "No", "Yes", "No", 
                                        "Yes", "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "No", 
                                        "No", "No", "Yes", "Yes", "No", "No", "Yes", "Yes", "No", "No", 
                                        "No", "No", "No", "Yes", "Yes", "No", "No", "Yes", "Yes", "No", 
                                        "No", "No", "Yes", "No", "No", "No", "No", "No", "No", "No", 
                                        "Yes", "No", "No", "No", "Yes", "Yes", "No", "No", "No", "No", 
                                        "No", "No", "No", "Yes", "Yes", "Yes", "No", "No", "Yes", "Yes", 
                                        "Yes", "Yes", "Yes", "No", "Yes", "Yes", "No", "No", "No", "No", 
                                        "No", "Yes", "No", "No", "No", "No", "No", "No", "Yes", "No", 
                                        "No", "Yes", "Yes", "No", "No", "No", "Yes", "No", "No", "No", 
                                        "No", "No", "Yes", "Yes", "No", "No", "No", "No", "No", "No", 
                                        "No", "No", "No", "Yes", "Yes", "Yes", "Yes", "No", "No", "Yes", 
                                        "Yes", "No", "Yes", "Yes", "Yes", "Yes", "No", "No", "Yes", "No", 
                                        "No", "Yes", "No", "No", "Yes", "Yes", "Yes", "No", "No", "Yes", 
                                        "Yes", "No", "No", "No", "No", "Yes", "Yes", "No", "No", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "Yes", "No", "No", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "No", "Yes", "No", "No", 
                                        "No", "Yes", "Yes", "No", "No", "No", "Yes", "Yes", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "No", "Yes", "Yes", "Yes", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "Yes", "No", "No", "No", 
                                        "No", "Yes", "Yes", "Yes", "Yes", "Yes", "No", "No", "No", "Yes", 
                                        "Yes", "No", "No", "Yes", "Yes", "Yes", "Yes", "No", "Yes", "Yes", 
                                        "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", "No", 
                                        "Yes", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                                        "No", "No", "No", "No", "No", "Yes", "Yes", "No", "Yes", "Yes", 
                                        "No", "No", "No", "No", "Yes", "No", "No", "Yes", "Yes", "Yes", 
                                        "Yes", "Yes", "No", "No", "No", "No", "Yes", "Yes", "Yes", "Yes", 
                                        "Yes", "Yes", "No", "No", "Yes", "Yes", "Yes", "Yes", "Yes", 
                                        "Yes", "No", "No", "Yes", "Yes", "No", "No", "No", "No", "No", 
                                        "Yes", "No", "No", "No", "Yes", "Yes", "No", "No", "No", "No", 
                                        "No", "No", "No", "No", "Yes", "No", "No", "No", "No", "Yes", 
                                        "Yes", "Yes", "No", "No", "No", "No", "No", "No", "No", "No", 
                                        "Yes", "Yes", "Yes", "Yes", "No", "No", "Yes", "Yes", "No", "No", 
                                        "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", "No", 
                                        "No", "No", "No", "No", "No", "No", "Yes", "Yes", "No", "No", 
                                        "No", "No", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes", "No", "No", 
                                        "No", "No", "Yes", "Yes", "Yes", "Yes", "Yes", "No", "Yes", "Yes", 
                                        "Yes", "No", "No", "Yes", "Yes", "Yes", "Yes", "Yes", "Yes")), 
    row.names = c(NA,-542L), 
    class = c("tbl_df", "tbl", "data.frame"))

还有我的对数似然函数


nll.18.4betas <- function(v) {
  #function(pi,beta) {
  pi <- v[1]; beta_o_v <- v[2]; beta_o_nv <- v[3]; beta_no_v <- v[4]; beta_no_nv <- v[5]
  
  data <- data4mle %>% 
    filter(Interval_18 > 0 & Interval_18 <= 180 & !is.na(Immune_status))
  
  #Owned, vaccinated/revaccinated
  xi_o_v <- data %>% 
    filter(Owned == "Yes" & Not_vacc_not_revacc_before_R3 == "Yes") %>% 
    .$Immune_status
  ti_o_v <- data %>% 
    filter(Owned == "Yes" & Not_vacc_not_revacc_before_R3 == "Yes") %>% 
    .$Interval_18
  
  #Owned, not vaccinated/revaccinated
  xi_o_nv <- data %>% 
    filter(Owned == "Yes" & Not_vacc_not_revacc_before_R3 == "No") %>% 
    .$Immune_status
  ti_o_nv <- data %>% 
    filter(Owned == "Yes" & Not_vacc_not_revacc_before_R3 == "No") %>% 
    .$Interval_18
  
  #Not owned, vaccinated/revaccinated
  xi_no_v <- data %>% 
    filter(Owned == "No" & Not_vacc_not_revacc_before_R3 == "Yes") %>% 
    .$Immune_status
  ti_no_v <- data %>% 
    filter(Owned == "No" & Not_vacc_not_revacc_before_R3 == "Yes") %>% 
    .$Interval_18
  
  ##Not owned, not vaccinated/revaccinated
  xi_no_nv <- data %>% 
    filter(Owned == "No" & Not_vacc_not_revacc_before_R3 == "No") %>% 
    .$Immune_status
  ti_no_nv <- data %>% 
    filter(Owned == "No" & Not_vacc_not_revacc_before_R3 == "No") %>% 
    .$Interval_18
  
  #calculate neg log likelihood
  #Owned, vaccinated/revaccinated
  -sum(xi_o_v*(log(pi)-beta_o_v*ti_o_v) + (1-xi_o_v)*log(1 - (pi*exp(-beta_o_v*ti_o_v)))) + 
    #Owned, not vaccinated/revaccinated
    -sum(xi_o_nv*(log(pi)-beta_o_nv*ti_o_nv) + (1-xi_o_nv)*log(1 - (pi*exp(-beta_o_nv*ti_o_nv)))) + 
    #Not owned, vaccinated/revaccinated
    -sum(xi_no_v*(log(pi)-beta_no_v*ti_no_v) + (1-xi_no_v)*log(1 - (pi*exp(-beta_no_v*ti_no_v)))) +
    #Not owned, not vaccinated/revaccinated
    -sum(xi_no_nv*(log(pi)-beta_no_nv*ti_no_nv) + (1-xi_no_nv)*log(1 - (pi*exp(-beta_no_nv*ti_no_nv))))
  
}

trial <- optim(fn = nll.18.4betas, par = c(0.1,  0.003,0.003,0.003, 0.003), 
               lower = c(0.1, rep(1e-3, 4)),
               upper = c(0.99,rep(1e-1, 4)), 
               method = "L-BFGS-B", hessian = T)

在尝试估计粗麻布时，我不断得到非有限差分误差，即使优化方法本身运行良好并生成五个参数的估计值（即当 hessian = FALSE 时）。我需要使用 L-BFGS-B，因为第一个参数 pi 是一个必须绑定在 0 和 1 之间的比例。

我查看了这个问题 (non-finite finite-difference value, many data become inf and NA after exponential) 中的建议，但据我了解，我需要使用 Nelder-Mead 方法来使用 numDeriv 包。

同样，对这个问题 (Optim: non-finite finite-difference value in L-BFGS-B) 的回复似乎不适用，我不确定这里讨论的内容是否与我的问题 (optim in r :non finite finite difference error) 直接相关。

我不确定这里发生了什么，特别是因为当我为具有六个参数（2 个 pi 和 4 个 beta）的嵌套模型运行优化时，“优化”能够生成粗麻布，因此我可以计算置信区间.

不确定这是否为某人提供了足够的信息来提供帮助，但如果有任何建议，我将不胜感激。 谢谢！

【问题讨论】：

  • 我尝试运行您的代码，但出现很多错误。我怀疑有些东西不见了。
  • 对不起@PaulSmith，我已经编辑了我的帖子以输入整个数据。希望现在有效

标签： r optimization


【解决方案1】：

根据您的限制，以下代码似乎产生了一个有效的解决方案：

set.seed(100)
trial <- optim(fn = nll.18.4betas, 
               par = runif(5), 
               method = "Nelder-Mead", hessian = T,
               control=list(maxit=5000))

# RESULT

$par
[1] 0.999362670 0.005248378 0.011744520 0.002088864 0.007242104

$value
[1] 258.8472

$counts
function gradient 
    1034       NA 

$convergence
[1] 0

$message
NULL

$hessian
            [,1]       [,2]       [,3]      [,4]       [,5]
[1,]    9811.427  -4834.189  -9284.515 -106446.3  -43436.32
[2,]   -4834.189 677710.202      0.000       0.0       0.00
[3,]   -9284.515      0.000 354806.186       0.0       0.00
[4,] -106446.252      0.000      0.000 9402389.7       0.00
[5,]  -43436.320      0.000      0.000       0.0 1259387.74

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