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delete a cell that reads an LP file
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‎tutorials/aqua/optimization/1_optimization_problems.ipynb‎

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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"# Quadratically Constrained Quadratic Programs"
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"# Quadratically Constrained Quadratic Programs\n",
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"The latest version of this notebook is available on https://github.com/Qiskit/qiskit/tree/master/docs/tutorials."
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"In this tutorial, we briefly introduce how to construct an optimization model with Qiskit Optimization.\n",
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"You can find detailed information at [Qiskit Aqua API references](https://qiskit.org/documentation/apidoc/optimization/optimization.html).\n",
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"\n",
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"Qiskit Optimization introduces `QuadraticProgram` class to make a model of an optimization problem.\n",
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"In this tutorial, we briefly introduce how to build optimization problems using Qiskit's optimization module.\n",
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"Qiskit introduces the `QuadraticProgram` class to make a model of an optimization problem.\n",
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"More precicely, it deals with quadratically constrained quadratic programs given as follows:\n",
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"\n",
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"$$\n",
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"\\begin{align}\n",
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"\\text{minimize}\\quad& x^\\top Q_0 x + c^\\top x \\\\\n",
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"\\text{subject to}\\quad& A x \\leq b \\\\\n",
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"& x^\\top Q_i x + a_i^\\top x \\leq r_i, \\quad 1,\\dots,i,\\dots,q \\\\\n",
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"\\text{minimize}\\quad& x^\\top Q_0 x + c^\\top x\\\\\n",
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"\\text{subject to}\\quad& A x \\leq b\\\\\n",
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"& x^\\top Q_i x + a_i^\\top x \\leq r_i, \\quad 1,\\dots,i,\\dots,q\\\\\n",
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"& l_i \\leq x_i \\leq u_i, \\quad 1,\\dots,i,\\dots,n,\n",
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"\\end{align}\n",
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"$$\n",
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"\n",
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"where the $Q_i$ are $n \\times n$ matrices, $A$ is a $m \\times n$ matrix , $x$, and $c$ are $n$-dimensional vectors, $b$ is an $m$-dimensional vector, and where $x$ can defined as binary, integer, or continuous variables.\n",
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"In addition to \"$\\leq$\" constraints 'QuadraticProgram' also supports \"$\\geq$\" and \"$=$\"."
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]
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Loading a Quadratic Program from an LP file"
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"## Loading a `Quadratic Program` from an LP file"
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]
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{
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"execution_count": 1,
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"metadata": {},
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"/opt/miniconda3/lib/python3.7/site-packages/qiskit_aqua-0.7.0-py3.7.egg/qiskit/aqua/operators/primitive_ops/pauli_op.py:25: DeprecationWarning: The module qiskit.extensions.standard is deprecated as of 0.14.0 and will be removed no earlier than 3 months after the release. You should import the standard gates from qiskit.circuit.library.standard_gates instead.\n",
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" from qiskit.extensions.standard import RZGate, RYGate, RXGate, XGate, YGate, ZGate, IGate\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"from qiskit.optimization import QuadraticProgram"
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"You start with an empty model or load a problem from LP files.\n",
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"You start with an empty model.\n",
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"You can display your optimization problem with a method `pprint_as_string` and `print_as_lp_string`."
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"\\ This file has been generated by DOcplex\n",
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"\\ ENCODING=ISO-8859-1\n",
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"\\Problem name: my problem\n",
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"\n",
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"Minimize\n",
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" obj: x - y + 10 z + [ x^2 - 2 y*z ]/2\n",
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"Subject To\n",
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" lin_eq: x + 2 y = 1\n",
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" lin_leq: x + 2 y <= 1\n",
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" lin_geq: x + 2 y >= 1\n",
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" quad_eq: [ x^2 - y*z + 2 z^2 ] + x + y = 1\n",
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" quad_leq: [ x^2 - y*z + 2 z^2 ] + x + y <= 1\n",
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" quad_geq: [ x^2 - y*z + 2 z^2 ] + x + y >= 1\n",
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"\n",
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"Bounds\n",
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" 0 <= x <= 1\n",
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" -1 <= y <= 5\n",
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" -1 <= z <= 5\n",
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"\n",
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"Binaries\n",
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" x\n",
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"\n",
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"Generals\n",
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" y\n",
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"End\n",
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"\n"
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]
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}
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],
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"source": [
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"# load an LP file\n",
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"mod = QuadraticProgram()\n",
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"mod.read_from_lp_file('aux_files/sample.lp')\n",
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"print(mod.export_as_lp_string())"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"Qiskit Optimization supports the conversion from Docplex model. You can easily make a model of an optimization problem with Docplex.\n",
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"Qiskit's optimization module supports the conversion from Docplex model. You can easily make a model of an optimization problem with Docplex.\n",
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"You can find the documentation of Docplex at https://ibmdecisionoptimization.github.io/docplex-doc/mp/index.html\n",
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"\n",
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"You can load a Docplex model to `QuadraticProgram` by invoking `from_docplex`."
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"## Loading a QuadraticProgram from a docplex model"
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"## Loading a `QuadraticProgram` from a docplex model"
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]
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"cell_type": "markdown",
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"source": [
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"## Directly constructing a QuadraticProgram"
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"## Directly constructing a `QuadraticProgram`"
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]
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"Qiskit Optimization stack supports three types of variables:\n",
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"The `QuadraticProgram` supports three types of variables:\n",
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"- Binary varible\n",
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"- Integer variable\n",
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"- Continuous variable\n",
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"<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>None</td></tr><tr><td>Terra</td><td>0.14.0</td></tr><tr><td>Aer</td><td>0.6.0</td></tr><tr><td>Ignis</td><td>0.3.0</td></tr><tr><td>Aqua</td><td>0.7.0</td></tr><tr><td>IBM Q Provider</td><td>0.6.1</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.7 (default, Mar 26 2020, 10:32:53) \n",
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