{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Unconstrained Optimization\n", "\n", "## Overview, Objectives, and Key Terms\n", "\n", "In [Lesson 21](L21_NonlinearEquations.ipynb), Newton's method solved equations by driving a residual to zero. Unconstrained optimization uses the same idea on a new residual: the derivative or gradient of an objective function.\n", "\n", "For one variable, an unconstrained optimum candidate satisfies\n", "\n", "$$\n", " f'(x)=0.\n", "$$\n", "\n", "For several variables, it satisfies\n", "\n", "$$\n", " \\nabla f(\\mathbf{x})=\\mathbf{0}.\n", "$$\n", "\n", "That makes the gradient from [Lesson 19](L19_NumericalDifferentiation.ipynb) the main bridge into optimization. This lesson focuses on unconstrained problems and `scipy.optimize.minimize`; constrained optimization is previewed only briefly because it is the topic of Lesson 23.\n", "\n", "### Objectives\n", "\n", "By the end of this lesson, you should be able to\n", "\n", "- Distinguish objective functions, design variables, local optima, and global optima.\n", "- Explain why unconstrained optimization can be viewed as root finding applied to derivatives or gradients.\n", "- Use gradient information to reason about a two-variable objective function.\n", "- Use `scipy.optimize.minimize` for one- and two-variable unconstrained problems.\n", "- Recognize constrained optimization as the next lesson's topic.\n", "\n", "### Key Terms\n", "\n", "- objective function\n", "- design variable\n", "- unconstrained optimization\n", "- local minimum and local maximum\n", "- global minimum and global maximum\n", "- stationary point\n", "- gradient vector\n", "- Hessian matrix\n", "- `scipy.optimize.minimize`\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Some Nomenclature\n", "\n", "Optimization problems often defined by minimizing an **objective function**\n", "\n", "$$\n", " \\min_{x} f(x) \\qquad \\text{or} \\qquad \\min_{\\mathbf{x}} f(\\mathbf{x}) \\, ,\n", "$$\n", "\n", "subject to the **inequality constraints**\n", "\n", "$$\n", " g(x) \\ge 0 \\qquad \\text{or} \\qquad \\mathbf{g(x)} \\ge \\mathbf{0} \\, ,\n", "$$\n", "\n", "and/or the **equality constraints**\n", "\n", "$$\n", " h(x) = 0 \\qquad \\text{or} \\qquad \\mathbf{h(x)} = \\mathbf{0} \\, .\n", "$$\n", "\n", "An optimization problem is *unconstrained* if it is subject to no inequality constraints and no equality constraints. Otherwise, the problem is *constrained*. In practice, unconstrained problems are often easier to solve using a variety of techniques for finding *extrema*. We'll start with unconstrained problems and then consider an important class of constrained problems known as *linear programs*." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Finding Extrema\n", "\n", "One of the great applications of differentiation is its ability\n", "to identify the *critical points* of a function $f(x)$, which\n", "include its *minima* and *maxima*, i.e., its *extrema*. Suppose\n", "$f(x)$ represents some quantity of interest, perhaps the cost \n", "of materials for some component or the signal-to-noise ratio of\n", "some sensor. If we want to minimize those costs or maximize those\n", "ratios, we need to use *optimization*. Although optimization problems\n", "and the techniques to solve them are quite diverse, we will stick to\n", "1-D problems in which the *objective function* to be minimized or \n", "maximized is continuous (as opposed to discrete).\n", "\n", "You've had calculus (and we've reviewed some its topics). Hence, you might recall that a function $f(x)$ exhibits an **extremum**, i.e., a **minimum** or **maximum**, at any point $x$ for which $f'(x)$ is zero and $f''(x)$ is nonzero. When $f'(x)$ *and* $f''(x)$ vanish, the point is often called a **saddle point**, though that term is more meaningful in multiple dimensions." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Exercise**: Given some fencing of *fixed* length `L`, what is the largest area that fencing can enclose if arranged in a rectangle of sides `a` and `b`? \n", "\n", "*Solution*:\n", "\n", "Here's the problem. We want to maximize $A = ab$ where $2a+2b = L$ or $b = L/2 - a$. We know $L$ and $b$ depends on $a$, so there is just one free parameter (i.e., we're in 1-D where we'll stay throughout). Note that $a$ (and $b$) can range from 0 to $L/2$.\n", "\n", "Formally, we see a solution to\n", "\n", "$$\n", " \\max_{a \\in [0,\\, L/2]} a\\left (\\frac{L}{2}-a \\right)\n", "$$\n", "\n", "which reads \"find the value of $a$ in the range $[0, L/2]$ that maximizes the quantity $f(a) = a(L/2-a)$. Here, $f(a)$ is the **objective function**.\n", "\n", "Differentiation of $f(a)$ gives\n", "\n", "$$\n", " f'(a) = L/2 - 2a \n", "$$\n", "\n", "which, when set to zero, requires that $a = L/4$. Consequently, $b = L/2-a = L/4 = a$. That is to say, our fence must form a square to maximize the area enclosed.\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Connection To Nonlinear Functions\n", "\n", "\n", "As the fence exercise illustrates, if we can write down the derivative and explicitly find the point at which it vanishes, our problem is solved. That is rarely the case. Often, the functions of interest have complicated derivatives that make $f'(x) = 0$ a nonlinear equation. We generally can't solve that problem directly. In many cases, we don't even have $f'(x)$, and at best, we can approximate it numerically using finite differences. \n", "\n", "Further complicating matters is that even if we can solve $f'(x)=0$, the result might not be an extremum (consider $f(x)=x^3$ and the zeros of its derivative $3x^2$), and it might not be unique. \n", "\n", "Consider the following example (for $f(x) = (\\sin(x^2)-3)^2$): " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:10.312543Z", "iopub.status.busy": "2026-07-05T19:00:10.312391Z", "iopub.status.idle": "2026-07-05T19:00:10.812373Z", "shell.execute_reply": "2026-07-05T19:00:10.811967Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import matplotlib\n", "%matplotlib inline\n", "import nonlinear_plots\n", "nonlinear_plots.extrema()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of the three roots, two correspond to minima---but the left one (blue circle) is greater than the right one (red square), so is it really a minimum? *Yes*, if we make the distinction between *local* and *global* minima. For this problem, the right minimum is the *global* minimum, while the central root (green star) represents a local maximum ($f(x)$ is *unbounded*, i.e., there is no value $M < \\infty$ such that $|f(x)| < M$ for all possible values of $x$). Given the choice, a global optimum is usually preferred, but for many cases, we're at best guaranteed a local minimum. There are techniques to increase our chances of finding a global optimum, but that's outside the present scope!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Solving Unconstrained Optimization Problems\n", "\n", "\n", "### When the Derivative is Available\n", "\n", "If we have $f(x)$ and can evaluate $f'(x)$, then either Newton's method or the secant method can be applied to $f'(x) = 0$. The same goes for multi-variable problems, where the gradient $\\nabla f(\\mathbf{x})$ replaces $f'(x)$, and the *Hessian* matrix $\\mathbf{H}(\\mathbf{x})$ replaces $f''(x)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Exercise**: Find the value of $x$ that maximizes the function $f(x) = 2\\sin(x) - x^2/10$ starting with $x_0 = 2.5$. Then, confirm your result by showing it on a graph of $f(x)$.\n", "\n", "*Solution*. We can immediately differentiate $f(x)$ to find $f'(x) = 2\\cos(x) + x/5$ and $f''(x) = -2\\sin(x) + 1/5$. Then, Newton's method gives" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:10.813460Z", "iopub.status.busy": "2026-07-05T19:00:10.813312Z", "iopub.status.idle": "2026-07-05T19:00:10.870103Z", "shell.execute_reply": "2026-07-05T19:00:10.869634Z" } }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "f = lambda z: 2*np.sin(z) - z**2/10 # objective function\n", "fp = lambda z: 2*np.cos(z) - z/5 \n", "fpp = lambda z: -2*np.sin(z) - 1/5 \n", "\n", "x = 2.5 # initial guess\n", "while abs(fp(x)) > 1e-12:\n", " x = x - fp(x)/fpp(x)\n", "\n", "x_vals = np.linspace(0, 5)\n", "plt.plot(x_vals, f(x_vals), 'k', label='f(x)')\n", "plt.plot(x_vals, fp(x_vals), 'g--', label=\"f'(x)\")\n", "plt.plot(x, f(x), 'rx', ms='20', label='optimum') # X marks the spot...\n", "plt.xlabel('x')\n", "plt.title('maximum values of f(x) is {:.2e} at x={:.2e}'.format(f(x), x))\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "
\n", "\n", "**Exercise**: Consider the objective function $f(\\mathbf{x}) = ax_0 + bx_1 - (2x_0^2 + x_0 x_1 + 2x_1^2)$. Compute $\\nabla f(\\mathbf{x})$ and $\\mathbf{H}(\\mathbf{x})$ (which is the jacobian of $\\mathbf{\\nabla g}(x)$. Then, for $a = 5$ and $b = 10$, determine the values of $x_0$ and $x_1$ that maximize $f(\\mathbf{x})$ starting with $\\mathbf{x} = [1, 2]^T$.\n", "\n", "*Solution*:\n", "\n", "The gradient is\n", "\n", "$$\n", "\\nabla f(\\mathbf{x}) = \n", "\\left [ \\begin{array}{c}\n", " \\partial f / \\partial x_0 \\\\\n", " \\partial f / \\partial x_1 \n", "\\end{array} \\right ] =\n", "\\left [ \\begin{array}{c}\n", " a - 4 x_0 - x_1 \\\\\n", " b - 4 x_1 - x_0\n", "\\end{array} \\right ] \\, .\n", "$$\n", "\n", "The Hessian matrix is the jacobian matrix for $\\mathbf{\\nabla f}(\\mathbf{x})$, or\n", "$$\n", "\\mathbf{H}(\\mathbf{x}) =\n", "\\left [ \\begin{array}{cc}\n", " \\partial \\nabla f_0 / \\partial x_0 & \\partial \\nabla f_0 / \\partial x_1 \\\\\n", " \\partial \\nabla f_1 / \\partial x_0 & \\partial \\nabla f_1 / \\partial x_1 \\\\\n", "\\end{array} \\right ] =\n", "\\left [ \\begin{array}{c}\n", " -4 & -1 \\\\\n", " -1 & -4\n", "\\end{array} \\right ] \\, .\n", "$$\n", "\n", "Now, apply Newton's method:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:10.871620Z", "iopub.status.busy": "2026-07-05T19:00:10.871530Z", "iopub.status.idle": "2026-07-05T19:00:11.014746Z", "shell.execute_reply": "2026-07-05T19:00:11.014312Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "f = lambda z: 5*z[0] + 10*z[1] - (2*z[0]**2 + z[0]*z[1] + 2*z[1]**2)\n", "gf = lambda z: np.array([5-4*x[0]-x[1], \n", " 10-4*x[1]-x[0]]) # gradient of f\n", "H = np.array([[-4.0, -1.0],\n", " [-1.0, -4.0]]) \n", "\n", "# Apply Newton's method\n", "x = np.array([1.0, 2.0])\n", "while sum(abs(gf(x))) > 1e-8:\n", " x = x - np.linalg.solve(H, gf(x))\n", " \n", "# Plot the results and show where the maximum exists\n", "x0, x1 = np.linspace(0, 5), np.linspace(0, 5)\n", "x0, x1 = np.meshgrid(x0, x1)\n", "plt.contourf(x0, x1, f([x0, x1]), 25)\n", "plt.colorbar()\n", "plt.plot(x[0], x[1], 'rx', ms=20)\n", "plt.xlabel('$x_0$')\n", "plt.ylabel('$x_1$')\n", "plt.title('$f(x_0, x_1)$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### When the Derivative is Unavailable\n", "\n", "If we have $f'(x)$, we can apply Newton's method to $f'(x) = 0$. Assuming we don't, how can we proceed? One option is to adapt the bisection method. Now, the search is not based on the change of the sign of $f(x)$ but rather it's magnitude relative to the left and right points. Again, we have to have isolated our (single) target value in some finite range, which may be no easy task (plotting helps). Alternatively, Newton-like methods can be used by approximating both $f'(x)$ and $f''(x)$ (or their multi-dimensional analogs) with finite differences." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gradients Make Optimization a Root-Finding Problem\n", "\n", "For one variable, a local optimum candidate satisfies $f'(x)=0$. For several variables, the condition becomes\n", "\n", "$$\n", " \\nabla f(\\mathbf{x})=\\mathbf{0}.\n", "$$\n", "\n", "This is why L21 and L22 sit naturally after L19: finite differences estimate derivatives and gradients, root finding drives residuals to zero, and optimization drives the gradient residual to zero.\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:11.015872Z", "iopub.status.busy": "2026-07-05T19:00:11.015776Z", "iopub.status.idle": "2026-07-05T19:00:11.126269Z", "shell.execute_reply": "2026-07-05T19:00:11.125583Z" } }, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "\n", "def objective(z):\n", " x, y = z\n", " return x**2 - x - 2*y - x*y + y**2\n", "\n", "\n", "def gradient(z):\n", " x, y = z\n", " return np.array([2*x - 1 - y, -2 - x + 2*y])\n", "\n", "x = np.linspace(-1.0, 3.0, 80)\n", "y = np.linspace(-1.0, 3.0, 80)\n", "X, Y = np.meshgrid(x, y)\n", "Z = objective((X, Y))\n", "\n", "point = np.array([0.0, 0.0])\n", "grad_point = gradient(point)\n", "\n", "plt.figure(figsize=(6.5, 4.8))\n", "levels = np.linspace(np.min(Z), np.max(Z), 25)\n", "contours = plt.contour(X, Y, Z, levels=levels)\n", "plt.clabel(contours, inline=True, fontsize=8)\n", "plt.quiver(point[0], point[1], -grad_point[0], -grad_point[1], color='C3', scale=8, width=0.008)\n", "plt.plot([1.6], [1.8], 'ko', label='minimum')\n", "plt.xlabel('$x_0$')\n", "plt.ylabel('$x_1$')\n", "plt.title('Negative gradient points downhill')\n", "plt.legend();\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Using `scipy.optimize.minimize`\n", "\n", "An alternative to Newton's method is the `minimize` function in `scipy.optimize`. From `help(minimize)`, we find\n", "\n", "```\n", "Help on function minimize in module scipy.optimize._minimize:\n", "\n", "minimize(fun, x0, args=(), method=None, jac=None, hess=None, hessp=None, bounds=None, constraints=(), \n", " tol=None, callback=None, options=None)\n", " Minimization of scalar function of one or more variables.\n", "```\n", "\n", "At a minimum, one must define (1) the function `fun` to minimize, and (2) an initial guess `x0` for the solution. The function minimize returns an *object* with several attributes, one of which is the solution `x`. Therefore, if one calls `sol = minimize(fun, x0)`, the solution is `sol.x`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "**Exercise**: Use `minimize` to find the *maximum* of $f(x) = 2\\sin(x) - x^2/10$ starting with $x_0 = 2.5$. \n", "\n", "**Solution**: Note that any maximization problem can be turned into a minimization problem negating the objective function, i.e., $f(x)$ becomes $-f(x)$. Then:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:11.127291Z", "iopub.status.busy": "2026-07-05T19:00:11.127192Z", "iopub.status.idle": "2026-07-05T19:00:11.203362Z", "shell.execute_reply": "2026-07-05T19:00:11.202837Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.42755179]\n" ] } ], "source": [ "import numpy as np\n", "from scipy.optimize import minimize\n", "f = lambda x: -2*np.sin(x) + x**2 / 10\n", "sol = minimize(f, x0=2.5)\n", "print(sol.x) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Example**: Use `minimize` to find $\\mathbf{x} = [x_0, x_1]^T$ that minimizes $f(x) =x_0^2 - x_0 - 2 x_1 - x_0 x_1 + x_1^2$. Use an initial guess of $x_0 = x_1 = 0$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution**:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "execution": { "iopub.execute_input": "2026-07-05T19:00:11.204393Z", "iopub.status.busy": "2026-07-05T19:00:11.204303Z", "iopub.status.idle": "2026-07-05T19:00:11.207705Z", "shell.execute_reply": "2026-07-05T19:00:11.207288Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.33333356 1.6666667 ]\n" ] } ], "source": [ "f = lambda x: x[0]**2 - x[0] -2*x[1] - x[0]*x[1] + x[1]**2\n", "x_initial = [0.0, 0.0]\n", "sol = minimize(f, x0=x_initial)\n", "print(sol.x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Preview: Constrained Optimization Comes Next\n", "\n", "Unconstrained optimization lets the search move anywhere in the design-variable space. Real engineering problems often add limits: nonnegative material amounts, maximum stress, fixed volume, budget, geometry, or safety margins.\n", "\n", "Those restrictions change the problem from\n", "\n", "$$\n", " \\min_{\\mathbf{x}} f(\\mathbf{x})\n", "$$\n", "\n", "to something like\n", "\n", "$$\n", " \\min_{\\mathbf{x}} f(\\mathbf{x}) \\quad \\text{subject to constraints on } \\mathbf{x}.\n", "$$\n", "\n", "That is the topic of Lesson 23. The main takeaway for this lesson is that unconstrained methods teach the objective, gradient, initial-guess, and result-object habits we will reuse once constraints enter the picture.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Further Reading\n", "\n", "Check out the [SciPy documentation](https://docs.scipy.org/doc/scipy/reference/optimize.html) on optimization and root finding." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.13.13" } }, "nbformat": 4, "nbformat_minor": 2 }