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//!
//! Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//!
//! File : gp1.rs
//!
//! Purpose: Demonstrates how to solve a simple Geometric Program (GP)
//! cast into conic form with exponential cones and log-sum-exp.
//!
//! Example from
//! https://gpkit.readthedocs.io/en/latest/examples.html//maximizing-the-volume-of-a-box
//!
extern crate mosek;
use mosek::{Task,Boundkey,Objsense,Streamtype,Soltype};
// Since the value of infinity is ignored, we define it solely
// for symbolic purposes
const INF : f64 = 0.0;
#[allow(non_snake_case)]
fn max_volume_box(Aw : f64,
Af : f64,
alpha : f64,
beta : f64,
gamma : f64,
delta : f64) -> Result<Vec<f64>,String>
{
let numvar = 3i32; // Variables in original problem
/* Create the optimization task. */
let mut task = match Task::new() {
Some(e) => e,
None => return Err("Failed to create task".to_string()),
}.with_callbacks();
// Directs the log task stream to the user specified
// method task_msg_obj.stream
task.put_stream_callback(Streamtype::LOG, |msg| print!("{}",msg))?;
// Add variables and constraints
task.append_vars(numvar)?;
let x = 0i32;
let y = 1i32;
let z = 2i32;
// Objective is the sum of three first variables
task.put_obj_sense(Objsense::MAXIMIZE)?;
task.put_c_slice(0, numvar, &[1.0,1.0,1.0])?;
task.put_var_bound_slice_const(0, numvar, Boundkey::FR, -INF, INF)?;
task.append_cons(3)?;
// s0+s1 < 1 <=> log(s0+s1) < 0
task.put_aij_list(&[0,0,1,1,2,2],
&[y, z, x, y, z, y],
&[1.0, 1.0, 1.0, -1.0, 1.0, -1.0])?;
task.put_con_bound(0,Boundkey::UP,-INF,Af.ln())?;
task.put_con_bound(1,Boundkey::RA,alpha.ln(),beta.ln())?;
task.put_con_bound(2,Boundkey::RA,gamma.ln(),delta.ln())?;
{
let afei = task.get_num_afe()?;
let u1 = task.get_num_var()?;
let u2 = u1+1;
let afeidx = &[0, 1, 2, 2, 3, 3, 5, 5];
let varidx = &[u1, u2, x, y, x, z, u1, u2];
let fval = &[1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0];
let gfull = &[0.0, 0.0, (2.0/Aw).ln(), (2.0/Aw).ln(), 1.0, -1.0];
task.append_vars(2)?;
task.append_afes(6)?;
task.put_var_bound_slice_const(u1, u1+2, Boundkey::FR, -INF, INF)?;
// Affine expressions appearing in affine conic constraints
// in this order:
// u1, u2, x+y+log(2/Awall), x+z+log(2/Awall), 1.0, u1+u2-1.0
task.put_afe_f_entry_list(afeidx, varidx, fval)?;
task.put_afe_g_slice(afei, afei+6, gfull)?;
{
let dom = task.append_primal_exp_cone_domain()?;
// (u1, 1, x+y+log(2/Awall)) \in EXP
task.append_acc(dom, &[0, 4, 2], &[0.0,0.0,0.0])?;
// (u2, 1, x+z+log(2/Awall)) \in EXP
task.append_acc(dom, &[1, 4, 3], &[0.0,0.0,0.0])?;
}
{
let dom = task.append_rzero_domain(1)?;
// The constraint u1+u2-1 \in \ZERO is added also as an ACC
task.append_acc(dom, &[5], &[0.0])?;
}
}
let _trm = task.optimize()?;
task.write_data("gp1.ptf")?;
let mut xyz = vec![0.0; 3];
task.get_xx_slice(Soltype::ITR, 0i32, numvar, xyz.as_mut_slice())?;
// task.write_data("gp1.ptf")?;
Ok(xyz.iter().map(|v| v.exp()).collect())
}
#[allow(non_snake_case)]
fn main() -> Result<(),String> {
// maximize h*w*d
// subjecto to 2*(h*w + h*d) <= Awall
// w*d <= Afloor
// alpha <= h/w <= beta
// gamma <= d/w <= delta
//
// Variable substitutions: h = exp(x), w = exp(y), d = exp(z).
//
// maximize x+y+z
// subject log( exp(x+y+log(2/Awall)) + exp(x+z+log(2/Awall)) ) <= 0
// y+z <= log(Afloor)
// log( alpha ) <= x-y <= log( beta )
// log( gamma ) <= z-y <= log( delta )
//
// Finally, the model we will implement:
//
// maximize x+y+z
// subject to s0 > exp(x+y+log(2/Awall); (s0,1,x+y+log(2/Awall)) in PEXP
// s1 > exp(x+z+log(2/Awall); (s1,1,x+z+log(2/Awall)) in PEXP
// s0+s1 < 1
//
// y+z < log Afloor
//
// x-y in [log alpha; log beta]
// z-y in [log gamma; log delta]
//
// (x,y,z) in pexp : x0 > x1 * exp(x2/x1)
let Aw = 200.0;
let Af = 50.0;
let alpha = 2.0;
let beta = 10.0;
let gamma = 2.0;
let delta = 10.0;
let hwd = max_volume_box(Aw, Af, alpha, beta, gamma, delta)?;
println!("h={:.4} w={:.4} d={:.4}\n", hwd[0], hwd[1], hwd[2]);
Ok(())
}
#[cfg(test)]
mod tests {
#[test]
fn test() {
super::main().unwrap();
}
}