test_exp.jl

using Convex
using Test

TOL = 1e-3

@testset "Exp Atoms" begin

  @testset "exp atom" begin
    y = Variable()
    p = minimize(exp(y), y>=0)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 1 atol=TOL
    @test evaluate(exp(y)) ≈ 1 atol=TOL

    y = Variable()
    p = minimize(exp(y), y>=1)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ exp(1) atol=TOL
    @test evaluate(exp(y)) ≈ exp(1) atol=TOL

    y = Variable(5)
    p = minimize(sum(exp(y)), y>=0)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 5 atol=TOL
    @test evaluate(sum(exp(y))) ≈ 5 atol=TOL

    y = Variable(5)
    p = minimize(sum(exp(y)), y>=0)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 5 atol=TOL
  end

  @testset "log atom" begin
    y = Variable()
    p = maximize(log(y), y<=1)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 0 atol=TOL

    y = Variable()
    p = maximize(log(y), y<=2)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ log(2) atol=TOL

    y = Variable()
    p = maximize(log(y), [y<=2, exp(y)<=10])
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ log(2) atol=TOL
  end

  @testset "log sum exp atom" begin
    y = Variable(5)
    p = minimize(logsumexp(y), y>=1)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ log(exp(1) * 5) atol=TOL
  end

  @testset "logistic loss atom" begin
    y = Variable(5)
    p = minimize(logisticloss(y), y>=1)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ log(exp(1) + 1) * 5 atol=TOL
  end

  @testset "entropy atom" begin
    y = Variable(5, Positive())
    p = maximize(entropy(y), sum(y)<=1)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ -(log(1 / 5)) atol=TOL
  end

  @testset "relative entropy atom" begin
    x = Variable(1)
    y = Variable(1)
    # x log (x/y)
    p = minimize(relative_entropy(x,y), y==1, x >= 2)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 2 * log(2) atol=TOL
  end

  @testset "log perspective atom" begin
    x = Variable(1)
    y = Variable(1)
    # y log (x/y)
    p = maximize(log_perspective(x,y), y==5, x <= 10)
    @test vexity(p) == ConvexVexity()
    solve!(p)
    @test p.optval ≈ 5 * log(2) atol=TOL
  end

end