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qcp.R
# Copyright 2020, Gurobi Optimization, LLC # # This example formulates and solves the following simple QCP model: # maximize # x # subject to # x + y + z = 1 # x^2 + y^2 <= z^2 (second-order cone) # x^2 <= yz (rotated second-order cone) # x, y, z non-negative library(gurobi) library(Matrix) model <- list() model$A <- matrix(c(1,1,1), nrow=1, byrow=T) model$modelsense <- 'max' model$obj <- c(1,0,0) model$rhs <- c(1) model$sense <- c('=') # First quadratic constraint: x^2 + y^2 - z^2 <= 0 qc1 <- list() qc1$Qc <- spMatrix(3, 3, c(1, 2, 3), c(1, 2, 3), c(1.0, 1.0, -1.0)) qc1$rhs <- 0.0 # Second quadratic constraint: x^2 - yz <= 0 qc2 <- list() qc2$Qc <- spMatrix(3, 3, c(1, 2), c(1, 3), c(1.0, -1.0)) qc2$rhs <- 0.0 model$quadcon <- list(qc1, qc2) result <- gurobi(model) print(result$objval) print(result$x) # Clear space rm(model, result)
