Tutorial_22b_Optimization_General.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Numerical Optimization\n",
    "\n",
    "This notebook uses the [Optim.jl](https://github.com/JuliaNLSolvers/Optim.jl) package which has general purpose routines for optimization. (Other packages that do similar things are [Optimization.jl](https://github.com/SciML/Optimization.jl), [NLopt.jl](https://github.com/JuliaOpt/NLopt.jl) and [JuMP.jl](https://github.com/JuliaOpt/JuMP.jl))\n",
    "\n",
    "The optimization problems are (for pedagogical reasons) the same as in the other notebook about optimization. This means that the solutions should be very similar and that the contour plots in the other notebook can be used as references.\n",
    "\n",
    "However, the current notebook is focused on methods for solving general optimization problems. In contrast, the other notebook focuses on linear-quadratic problems (mean-variance, least squares, etc), where there are faster algorithms. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load Packages and Extra Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Printf, Optim\n",
    "\n",
    "include(\"src/printmat.jl\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots\n",
    "default(size = (480,320),fmt = :png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization with One Choice Variable\n",
    "\n",
    "Running \n",
    "```\n",
    "Sol = optimize(x->fn1(x,0.5),a,b)\n",
    "```\n",
    "finds the `x` value (in the interval `[a,b]`) that *minimizes* `fn1(x,0.5)`. The `x->fn1(x,0.5)` syntax makes this a function of `x` only, which is what the `optimize() function` wants.\n",
    "\n",
    "The output (`Sol`) contains a lot of information."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fn1 (generic function with 1 method)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fn1(x,c)                    #notice: the function has two arguments\n",
    "  value = 2*(x - 1.1)^2 - c\n",
    "  return value\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = -1:0.1:3\n",
    "\n",
    "p1 = plot( x,fn1.(x,0.5),                 #plotting the function can help identify\n",
    "           linecolor = :red,              #starting points and possible issues\n",
    "           linewidth = 1,\n",
    "           legend = nothing,\n",
    "           title = \"the fn1(x,0.5) function\",\n",
    "           xlabel = \"x\",\n",
    "           ylabel = \"y\" )\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Results of Optimization Algorithm\n",
      " * Status: success\n",
      " * Algorithm: Brent's Method\n",
      " * Search Interval: [-2.000000, 3.000000]\n",
      " * Minimizer: 1.100000e+00\n",
      " * Minimum: -5.000000e-01\n",
      " * Iterations: 5\n",
      " * Convergence: max(|x - x_upper|, |x - x_lower|) <= 2*(1.5e-08*|x|+2.2e-16): true\n",
      " * Objective Function Calls: 6\n",
      "\n",
      "\u001b[34m\u001b[1mThe minimum is at: \u001b[22m\u001b[39m\u001b[34m\u001b[1m1.1\u001b[22m\u001b[39m\n",
      "\u001b[34m\u001b[1mCompare with the plot above\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "Sol = optimize(x->fn1(x,0.5),-2.0,3.0)\n",
    "println(Sol)\n",
    "\n",
    "printblue(\"\\nThe minimum is at: \", Optim.minimizer(Sol))     #the optimal x value\n",
    "printblue(\"Compare with the plot above\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## One Choice Variable: Supplying a Starting Guess Instead (extra)\n",
    "\n",
    "If you prefer to give a starting guess `c` instead of an interval, then supply it as as a vector `[c]`. The solution is then also a vector (with one element.)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The minimum is at:      1.100\n"
     ]
    }
   ],
   "source": [
    "Solb = optimize(x->fn1(x[],0.5),[0.1])\n",
    "\n",
    "printlnPs(\"The minimum is at: \",Optim.minimizer(Solb))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Several Choice Variables: Unconstrained Optimization\n",
    "\n",
    "In the example below, we choose $(x,y)$ so as to minimize the fairly simple objective function\n",
    "\n",
    "$\n",
    "(x-2)^2 + (4y+3)^2,  \n",
    "$\n",
    "\n",
    "without any constraints. The solution should be $(x,y)=(2,-3/4)$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "fn2 (generic function with 1 method)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function fn2(θ)\n",
    "    (x,y) = (θ[1],θ[2])          #unpack the choice variables and get nicer names\n",
    "     L    = (x-2)^2 + (4*y+3)^2\n",
    "    return L\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "minimum at (x,y)=      2.000    -0.750\n"
     ]
    }
   ],
   "source": [
    "θ₀ = [4.0,-0.5]               #starting guess\n",
    "\n",
    "Sol = optimize(fn2,θ₀)        #use θ->lossfn(θ,other arguments) if there are\n",
    "                              #additional (non-choice) function arguments\n",
    "printlnPs(\"minimum at (x,y)= \",Optim.minimizer(Sol))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Several Choice Variables: Bounds on the Solutions\n",
    "\n",
    "The next few cells discuss how to impose bounds on the solution.\n",
    "\n",
    "In the example below, we impose $2.75 \\leq x$ (a lower bound) and $y \\leq -0.3$ (an upper bound). We will see that only one of these restrictions binds."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The optimum is at (x,y) =      2.750    -0.750\n"
     ]
    }
   ],
   "source": [
    "lower_θ = [2.75, -Inf]\n",
    "upper_θ = [Inf, -0.3]\n",
    "\n",
    "Sol = optimize(fn2,lower_θ,upper_θ,θ₀)\n",
    "printlnPs(\"The optimum is at (x,y) = \",Optim.minimizer(Sol))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Several Choice Variables: Equality Restrictions (extra)\n",
    "\n",
    "We now impose the constraint that $x+2y-3=0$ (that is, $y=1.5-0.5x$) The `Optim.jl` package can handle both equality and inequality constraints, but the syntax is a bit more involved than in the earlier examples. The remarks below discuss this. (Clearly, we could handle this single linear equality constraint by rewriting the objecive function instead, so consider this as just a simple illustration.) The solution should be at $(x,y)=(4,-0.5)$\n",
    "\n",
    "### Remarks on the Code\n",
    "\n",
    "1. `TwiceDifferentiable(fn2,θ₀)` and `TwiceDifferentiableConstraints(EqConstrfun!,lower_θ,upper_θ,lower_c,upper_c)` tell the `optimize()` function that the objective function and constraint are differentiable (twice).\n",
    "\n",
    "2. The function for the constraint (`EqConstrfun!(c,θ)`) takes two inputs: `c` will be filled (by `optimize()`) with the calculations in the function and `θ` is the vector of choice variables.\n",
    "\n",
    "3. `lower_θ` and `upper_θ` are (vectors of) bounds on the choice variables. With no bounds, use `[-Inf,-Inf]` and `[Inf,Inf]`.\n",
    "\n",
    "4. `lower_c` and `upper_c` are (vectors of) bounds on the output from the constraint function. With a single equality constraint, use `[0.0]` for both."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constrained, x+2y-3=0\n",
      "     4.000    -0.500\n"
     ]
    }
   ],
   "source": [
    "function EqConstrfun!(c,θ)       #a function for a constraint\n",
    "    (x,y) = (θ[1],θ[2])          #c is an array where results are written to\n",
    "    c[1]  = x + 2*y - 3          #update the input c\n",
    "    return c\n",
    "end\n",
    "\n",
    "lower_θ = [-Inf,-Inf]                 #effectively no bounds on the parameters, but needed\n",
    "upper_θ = [Inf,  Inf]\n",
    "lower_c = [0.0]                       #c from EqConstrfun! should be lower_c <= c <= upper_c\n",
    "upper_c = [0.0]\n",
    "\n",
    "df  = TwiceDifferentiable(fn2,θ₀)       #informing about the differentiability of the problem\n",
    "dfc = TwiceDifferentiableConstraints(EqConstrfun!,lower_θ,upper_θ,lower_c,upper_c)\n",
    "Sol = optimize(df,dfc,θ₀,IPNewton())\n",
    "println(\"Constrained, x+2y-3=0\")\n",
    "printlnPs(Optim.minimizer(Sol))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Optimization with Inequality Constraints (extra)\n",
    "\n",
    "We now impose the non-linear constraint that $y \\le -(x-4)^2$, that is, $y + (x-4)^2 \\le 0$.\n",
    "\n",
    "This is very similar to the linear constraint above, except that we need a new constraint function and that `lower_c = [-Inf]` and `upper_c = [0.0]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\" />"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx = 2*41\n",
    "ny = 2*61\n",
    "x = range(1,5,length=nx)\n",
    "y = range(-1,0,length=ny)\n",
    "\n",
    "loss2d = fill(NaN,(nx,ny))      #matrix with loss fn values\n",
    "for i in 1:nx, j in 1:ny\n",
    "    loss2d[i,j] = fn2([x[i];y[j]])\n",
    "end\n",
    "\n",
    "yRestriction = -(x.-4).^2               #y should be less than this\n",
    "\n",
    "p1 = contour( x,y,loss2d',\n",
    "              legend = false,\n",
    "              levels = 21,\n",
    "              title = \"Contour plot of loss function\",\n",
    "              xlabel = \"x\",\n",
    "              ylabel = \"y\",\n",
    "              xlims = (1,5),\n",
    "              ylims = (-1,0),\n",
    "              annotation = (4.0,-0.7,text(\"somewhere here\",8)) )\n",
    "plot!(x,yRestriction,linecolor=:red,linewidth=1,label=\"y is below this curve\")\n",
    "scatter!([3.1],[-0.79],markercolor=:red,label=\"optimum\",legend=:topleft)\n",
    "display(p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Constrained, y + (x-4)^2 <= 0\n",
      "     3.112    -0.789\n"
     ]
    }
   ],
   "source": [
    "function IneqConstrfun!(c,θ)            #another restriction\n",
    "    (x,y) = (θ[1],θ[2])\n",
    "    c[1]  = y + (x-4)^2                 #lower_c <= c[1] <= upper_c\n",
    "  return c\n",
    "end\n",
    "\n",
    "lower_θ = [-Inf,-Inf]                   #effectively no bounds on the parameters\n",
    "upper_θ = [Inf,Inf]\n",
    "lower_c = [-Inf]                        # -Inf <= c <= 0.0\n",
    "upper_c = [0.0]\n",
    "\n",
    "df  = TwiceDifferentiable(fn2,θ₀)\n",
    "dfc = TwiceDifferentiableConstraints(IneqConstrfun!,lower_θ,upper_θ,lower_c,upper_c)\n",
    "Sol = optimize(df,dfc,θ₀,IPNewton())\n",
    "println(\"Constrained, y + (x-4)^2 <= 0\")\n",
    "printlnPs(Optim.minimizer(Sol))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Several Choice Variables:  Supplying the Gradient (extra)\n",
    "\n",
    "Supplying a function for calculating the derivatives improves speed and accuracy. See below for an example."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " * Status: success\n",
      "\n",
      " * Candidate solution\n",
      "    Final objective value:     9.860761e-30\n",
      "\n",
      " * Found with\n",
      "    Algorithm:     L-BFGS\n",
      "\n",
      " * Convergence measures\n",
      "    |x - x'|               = 9.34e-01 ≰ 0.0e+00\n",
      "    |x - x'|/|x'|          = 4.67e-01 ≰ 0.0e+00\n",
      "    |f(x) - f(x')|         = 8.75e-01 ≰ 0.0e+00\n",
      "    |f(x) - f(x')|/|f(x')| = 8.88e+28 ≰ 0.0e+00\n",
      "    |g(x)|                 = 2.49e-14 ≤ 1.0e-08\n",
      "\n",
      " * Work counters\n",
      "    Seconds run:   0  (vs limit Inf)\n",
      "    Iterations:    2\n",
      "    f(x) calls:    7\n",
      "    ∇f(x) calls:   7\n",
      "\n",
      "\u001b[34m\u001b[1mProbably faster than the solution above\u001b[22m\u001b[39m\n",
      "\u001b[34m\u001b[1mMinimum at: \u001b[22m\u001b[39m\u001b[34m\u001b[1m[2.0, -0.75]\u001b[22m\u001b[39m\n"
     ]
    }
   ],
   "source": [
    "function g2!(G,θ)                        #derivatives of fn2 wrt. θ[1] and θ[2]\n",
    "    (x,y) = (θ[1],θ[2])\n",
    "    G[:] = [2*(x-2), 2*4*(4*y+3)]        #fills/updates an existing vector\n",
    "    return G\n",
    "end\n",
    "\n",
    "Sol3 = optimize(fn2,g2!,[1.0,-0.5])\n",
    "println(Sol3)\n",
    "printblue(\"Probably faster than the solution above\")\n",
    "printblue(\"Minimum at: \",round.(Optim.minimizer(Sol3),digits=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "@webio": {
   "lastCommId": null,
   "lastKernelId": null
  },
  "anaconda-cloud": {},
  "kernel_info": {
   "name": "julia-1.2"
  },
  "kernelspec": {
   "display_name": "Julia 1.11.1",
   "language": "julia",
   "name": "julia-1.11"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "1.11.1"
  },
  "nteract": {
   "version": "0.15.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}