# Global optimization of up to cubic polynomial functions (up to 5 variables) Optimize a quadratic or cubic polynomial functionin 2 ~ 5 variables with bound constraints if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="DelCastilloCR",package="OptimaRegion",cached_env=.Rdpack.currefs) . ```r GloptiPolyR(P) ``` ## Arguments - `P`: A list of list; Each sub-list has 2 components: 1. a multi-dimensional array corresponding to a objective or constraint function 2. an attribute of the objective or constraint function ## Returns Returns the optimal solution and its corresponding objective value ## Details GloptipolyR is an R implementation of the “Gloptipoly” algorithm if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="lasserre2001global",package="OptimaRegion",cached_env=.Rdpack.currefs) ## Author(s) Enrique del Castillo exd13@psu.edu , Peng Chen pfc5098@psu.edu , Adam Meyers akm5733@psu.edu , John Hunt J.Hunt@westernsydney.edu.au and James Rapkin jr297@exeter.ac.uk . ## Examples ```r # Optimize the following quadratic function in 3 variables # f(x) = -1.5 x_1 + 2.13 x_2 - 1.81 x_3 + 7.13 x_1 x_2 + # 3.27 x_1 x_3 + 2.73 x_2 x_3 + # 4.69 x_1^2 + 6.27 x_2^2 + 5.21 x_3^2. # The input for GloptiPolyR is a list of 7 sub-lists, # each of which corresponds to the objective function or a constraint # function, respectively. See del Castillo et al. (2019) for details. P <- list() p_f <- list() p_g_1 <- list() p_g_2 <- list() p_g_3 <- list() p_g_4 <- list() p_g_5 <- list() p_g_6 <- list() p_f$c <- array(0, dim = c(3, 3, 3)) p_f$c[2, 1, 1] <- -1.5 p_f$c[1, 2, 1] <- 2.13 p_f$c[1, 1, 2] <- -1.81 p_f$c[2, 2, 1] <- 7.13 p_f$c[2, 1, 2] <- 3.27 p_f$c[1, 2, 2] <- 2.73 p_f$c[3, 1, 1] <- 4.69 p_f$c[1, 3, 1] <- 6.27 p_f$c[1, 1, 3] <- 5.21 p_g_1$c <- array(0, dim = c(3, 3, 3)) p_g_1$c[1, 1, 1] <- 2 p_g_1$c[2, 1, 1] <- 1 p_g_2$c <- array(0, dim = c(3, 3, 3)) p_g_2$c[1, 1, 1] <- -2 p_g_2$c[2, 1, 1] <- 1 p_g_3$c <- array(0, dim = c(3, 3, 3)) p_g_3$c[1, 1, 1] <- 2 p_g_3$c[1, 2, 1] <- 1 p_g_4$c <- array(0, dim = c(3, 3, 3)) p_g_4$c[1, 1, 1] <- -2 p_g_4$c[1, 2, 1] <- 1 p_g_5$c <- array(0, dim = c(3, 3, 3)) p_g_5$c[1, 1, 1] <- 2 p_g_5$c[1, 1, 2] <- 1 p_g_6$c <- array(0, dim = c(3, 3, 3)) p_g_6$c[1, 1, 1] <- -2 p_g_6$c[1, 1, 2] <- 1 # Set the attribute for the objective function as either ``min'' or ``max''. p_f$t <- "min" # Set the attributes for the constraint functions as either ``>='' or ``<=''. p_g_1$t <- ">=" p_g_2$t <- "<=" p_g_3$t <- ">=" p_g_4$t <- "<=" p_g_5$t <- ">=" p_g_6$t <- "<=" # Now we put together the input P and use it to call GloptiPolyR P <- list(p_f, p_g_1, p_g_2, p_g_3, p_g_4, p_g_5, p_g_6) GloptiPolyR(P) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs)

GloptiPolyR function