Difference between revisions of "MIPDECO"
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| − | === Parabolic Robin Boundary Problem in One Dimension === | + | === Parabolic Robin Boundary Problem in One Spatial Dimension === |
| + | This model is modified from OPTPDE library (http://www.optpde.uni-hamburg.de/result.php?id=8). The goal is to find the optimal state and control variables that satisfy the Heat equation with boundary conditions. There are two classes of models: one with binary controls, and one with controls in [-1,0,1]. Both L1 and L2 regularizations are used. | ||
| − | === Parabolic Robin Boundary Problem in Two Dimensions === | + | {| border="1" cellpadding="1" cellspacing="1" |
| + | |- align="left" | ||
| + | | '''Type of PDE''' | ||
| + | | Heat equation on [0,1] with REobin and Neuman boundary conditions | ||
| + | |- | ||
| + | | '''Class of Integers''' | ||
| + | | Mesh-dependent & mesh-independent binary variables | ||
| + | |- | ||
| + | | '''Type of Objective''' | ||
| + | | Least-squares (inverse problem) with L1 or L2 regularization term | ||
| + | |- | ||
| + | | '''Type of Constraints''' | ||
| + | | Binary or integer controls | ||
| + | |- | ||
| + | | '''Discretization''' | ||
| + | | Crank-Nicolson formula | ||
| + | |} | ||
| + | |||
| + | === Parabolic Robin Boundary Problem in Two Spatial Dimensions === | ||
Revision as of 14:34, 17 March 2017
Mixed-Integer PDE Constrained Optimization (MIPDECO) Test Problems
This page links to sets of MIPDECO test problems written in AMPL and described in a companion report.
Each problem includes a characterization in terms of type of PDE, class of integers, type of objective, type of constraints, and discretization scheme.
A tar-ball with all ampl models, data, and command files is available here. A tar-ball with the corresponding stub.nl files is available here.
Laplace Source Inversion
Problem is to identify source to match an observed state, governed by Laplace equation with Dirichtlet boundary conditions.
| Type of PDE | Laplace equation on [0,1]^2 with Dirichlet boundary conditions |
| Class of Integers | Mesh-dependent & mesh-independent binary variables |
| Type of Objective | Least-squares (inverse problem) with possible regularization term |
| Type of Constraints | Knapsack constraint on binary variables |
| Discretization | Five-point finite difference stencil |
Distributed Control with Neumann Boundary Conditions
Parabolic Robin Boundary Problem in One Spatial Dimension
This model is modified from OPTPDE library (http://www.optpde.uni-hamburg.de/result.php?id=8). The goal is to find the optimal state and control variables that satisfy the Heat equation with boundary conditions. There are two classes of models: one with binary controls, and one with controls in [-1,0,1]. Both L1 and L2 regularizations are used.
| Type of PDE | Heat equation on [0,1] with REobin and Neuman boundary conditions |
| Class of Integers | Mesh-dependent & mesh-independent binary variables |
| Type of Objective | Least-squares (inverse problem) with L1 or L2 regularization term |
| Type of Constraints | Binary or integer controls |
| Discretization | Crank-Nicolson formula |