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Merge pull request #60 from ndcbe/contributed-notebooks
Contributions for Project 2
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Diff for: _toc.yml

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Diff for: notebooks/4-dev/AdvancedTopics.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"### Sample Average Approximation\n",
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"## Sample Average Approximation\n",
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"\n",
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"Sample average approximation (SAA) method is an approach for solving stochastic optimization problems by Monte Carlo simulation. It approximates the expected objective function of the stochastic problem by a sample average estimate derived from a random sample. The resulting sample average approximation problem is then solved by deterministic optimization techniques. \n",
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"cell_type": "markdown",
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"### Sparse Grids (Worst Case)\n",
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"## Sparse Grids (Worst Case)\n",
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"\n",
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"Instead of Monte carlo sampling, sparse grids can be used to obtain efficient characterizations of the integrals in stochastic programs. Many computational problems are solved on full grids. While this is feasible if the dimentionality $d$ of the problem is low, 2 or 3, full grids become very expensive when facing a higher dimentional problem $d>4$. This is due to the curse of dimensionality, which states that the complexity of full grids grows exponentially with $d$. \n",
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"cell_type": "markdown",
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"metadata": {},
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"### Reference \n",
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"## Reference \n",
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"\n",
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"Biegler, L.T., 2010. Nonlinear programming: concepts, algorithms, and applications to chemical processes. Society for Industrial and Applied Mathematics.\n",
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"\n",

Diff for: notebooks/4/AdvancedTopics.ipynb

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"cell_type": "markdown",
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"metadata": {},
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"### Sample Average Approximation\n",
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"## Sample Average Approximation\n",
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"\n",
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"Sample average approximation (SAA) method is an approach for solving stochastic optimization problems by Monte Carlo simulation. It approximates the expected objective function of the stochastic problem by a sample average estimate derived from a random sample. The resulting sample average approximation problem is then solved by deterministic optimization techniques. \n",
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"\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Sparse Grids (Worst Case)\n",
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"## Sparse Grids (Worst Case)\n",
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"\n",
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"Instead of Monte carlo sampling, sparse grids can be used to obtain efficient characterizations of the integrals in stochastic programs. Many computational problems are solved on full grids. While this is feasible if the dimentionality $d$ of the problem is low, 2 or 3, full grids become very expensive when facing a higher dimentional problem $d>4$. This is due to the curse of dimensionality, which states that the complexity of full grids grows exponentially with $d$. \n",
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"\n",
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Reference \n",
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"## Reference \n",
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"\n",
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"Biegler, L.T., 2010. Nonlinear programming: concepts, algorithms, and applications to chemical processes. Society for Industrial and Applied Mathematics.\n",
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"\n",

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