Difference between revisions of "MIPDECO"

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=== Parabolic Robin Boundary Problem in One Dimension ===
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=== Parabolic Robin Boundary Problem in One Spatial Dimension ===
  
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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 ===
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{| border="1" cellpadding="1" cellspacing="1"
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|- align="left"
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| '''Type of PDE'''
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| Heat equation on [0,1] with REobin and Neuman boundary conditions
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|-
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| '''Class of Integers'''
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| Mesh-dependent & mesh-independent binary variables
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|-
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| '''Type of Objective'''
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| Least-squares (inverse problem) with L1 or L2 regularization term
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|-
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| '''Type of Constraints'''
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| Binary or integer controls
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|-
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| '''Discretization'''
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|  Crank-Nicolson formula
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|}
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=== Parabolic Robin Boundary Problem in Two Spatial Dimensions ===
  
  

Revision as of 15:34, 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

Parabolic Robin Boundary Problem in Two Spatial Dimensions

Heat Equation Actuator-Placement

Subsurface Flow Well-Placement