\n",
"\n",
"show code\n",
"\"\"\")"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"hide_input": true,
"scrolled": true
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" show code\n",
" "
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%run ./loadoptfuncs.py\n",
"toggle()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Nonlinear Programming"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In many optimization models the objective and/or the constraints are nonlinear functions of the decision variables. Such an optimization model is called a nonlinear programming (NLP) model.\n",
"\n",
"- When you solve an LP model, you are mostly guaranteed that the solution obtained is an optimal solution and a sensitivity analysis with shadow price and reduced cost is available.\n",
"\n",
"- When you solve an NLP model, it is very possible that you obtain a suboptimal solution.\n",
"\n",
"This is because a nonlinear function can have local optimal solutions where\n",
"\n",
"- a local optimum is better than all nearby points\n",
"\n",
"that are not the global optimal solution\n",
"\n",
"- a global optimum is the best point in the entire feasible region"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
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