Difference between revisions of "MIPDECO"

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Line 7: Line 7:
 
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.
 
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 ===
+
= Laplace Source Inversion =
  
 
Problem is to identify source to match an observed state, governed by Laplace equation with Dirichtlet boundary conditions.
 
Problem is to identify source to match an observed state, governed by Laplace equation with Dirichtlet boundary conditions.
Line 29: Line 29:
 
|}
 
|}
  
−
=== Distributed Control with Neumann Boundary Conditions ===
+
 
 +
{| border="1" cellpadding="1" cellspacing="1"
 +
|- align="left"
 +
!  NAME
 +
!  mod file
 +
!  dat file
 +
!  mesh
 +
!  optimal objective
 +
|-
 +
|  SrcDetct-MeshDep-008-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-008-1.dat|MeshDep-008-1.dat]]
 +
|  8x8
 +
|  0.0022
 +
|-
 +
|  SrcDetct-MeshDep-008-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-008-2.dat|MeshDep-008-2.dat]]
 +
|  8x8
 +
|  0.0001
 +
|-
 +
|  SrcDetct-MeshDep-008-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-008-3.dat|MeshDep-008-3.dat]]
 +
|  8x8
 +
|  0.0001
 +
|-
 +
|  SrcDetct-MeshDep-016-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-016-1.dat|MeshDep-016-1.dat]]
 +
|  16x16
 +
|  0.0076
 +
|-
 +
|  SrcDetct-MeshDep-016-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-016-2.dat|MeshDep-016-2.dat]]
 +
|  16x16
 +
|  0.0000
 +
|-
 +
|  SrcDetct-MeshDep-016-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-016-3.dat|MeshDep-016-3.dat]]
 +
|  16x16
 +
|  0.5675
 +
|-
 +
|  SrcDetct-MeshDep-032-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-032-1.dat|MeshDep-032-1.dat]]
 +
|  32x32
 +
|  0.0298
 +
|-
 +
|  SrcDetct-MeshDep-032-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-032-2.dat|MeshDep-032-2.dat]]
 +
|  32x32
 +
|  0.0000
 +
|-
 +
|  SrcDetct-MeshDep-032-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshDep-032-3.dat|MeshDep-032-3.dat]]
 +
|  32x32
 +
|  2.2180
 +
|-
 +
|  SrcDetct-MeshInd-008-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-008-1.dat|MeshInd-008-1.dat]]
 +
|  8x8
 +
|  0.0002
 +
|-
 +
|  SrcDetct-MeshInd-008-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-008-2.dat|MeshInd-008-2.dat]]
 +
|  8x8
 +
|  0.0001
 +
|-
 +
|  SrcDetct-MeshInd-008-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-008-3.dat|MeshInd-008-3.dat]]
 +
|  8x8
 +
|  0.0001
 +
|-
 +
|  SrcDetct-MeshInd-016-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-016-1.dat|MeshInd-016-1.dat]]
 +
|  16x16
 +
|  0.0006
 +
|-
 +
|  SrcDetct-MeshInd-016-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-016-2.dat|MeshInd-016-2.dat]]
 +
|  16x16
 +
|  0.0004
 +
|-
 +
|  SrcDetct-MeshInd-016-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-016-3.dat|MeshInd-016-3.dat]]
 +
|  16x16
 +
|  0.3271
 +
|-
 +
|  SrcDetct-MeshInd-032-1
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-032-1.dat|MeshInd-032-1.dat]]
 +
|  32x32
 +
|  0.0023
 +
|-
 +
|  SrcDetct-MeshInd-032-2
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-032-2.dat|MeshInd-032-2.dat]]
 +
|  32x32
 +
|  0.0015
 +
|-
 +
|  SrcDetct-MeshInd-032-3
 +
| [[Media:SrcDetct.mod|SrcDetct.mod]]
 +
| [[Media:MeshInd-032-3.dat|MeshInd-032-3.dat]]
 +
|  32x32
 +
|  1.3068
 +
|-
 +
|+ align="bottom" | MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension
 +
|}
 +
 
 +
 
 +
In this problem, the state variables, u, can be eliminated, resulting in a pure integer QP. The model that defines the problems without state variables is [[Media:SrcDetctElim.mod|SrcDetctElim.mod]], and the AMPL script, [[Media:Presolve.ampl|Presolve.ampl]] implements the presolve step. The calling sequence is
 +
 
 +
<code> ampl: model SrcDetctElim.mod; data MeshDep-008-1.dat; include Presolve.ampl; </code>
 +
 
 +
for the small example, SrcDetct-MeshDep-008-1.
 +
 
 +
= The Mother Problem: Distributed Control with Neumann Boundary Conditions =
 +
 
 +
The objective is to find optimal control and state variables for an optimal control problem that has Poisson equation with a potential term and Neumann boundary conditions. Control variables are treated as binary variables.
 +
 
 +
'''Source''': Continuous form taken from OPTPDE library Problem ccdist1 submitted by Roland Herzog, see http://www.optpde.uni-hamburg.de/result.php?id=2
 +
 
 +
{| border="1" cellpadding="1" cellspacing="1"
 +
|- align="left"
 +
| '''Type of PDE'''
 +
| Poisson equation with a potential term on [01]x[0,1] with 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'''
 +
|  Five-point finite-difference stencil
 +
|}
  
  
−
=== Parabolic Robin Boundary Problem in One Spatial Dimension ===
+
 
 +
{| border="1" cellpadding="1" cellspacing="1"
 +
|- align="left"
 +
!  NAME
 +
!  mod file
 +
!  dat file
 +
!  mesh
 +
!  optimal objective
 +
|-
 +
|  MotherProbL1-md008
 +
| [[Media:MotherProbL1.mod|MotherProbL1.mod]]
 +
| [[Media:md008.dat|md008.dat]]
 +
|  8x8
 +
|  1274.4697
 +
|-
 +
|  MotherProbL1-md016
 +
| [[Media:MotherProbL1.mod|MotherProbL1.mod]]
 +
| [[Media:md016.dat|md016.dat]]
 +
|  16x16
 +
|  1148.5152
 +
|-
 +
|  MotherProbL1-md032
 +
| [[Media:MotherProbL1.mod|MotherProbL1.mod]]
 +
| [[Media:md032.dat|md032.dat]]
 +
|  32x32
 +
|  1087.0657
 +
|-
 +
|  MotherProbL1-mi008a
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi008a.dat|mi008a.dat]]
 +
|  8x8
 +
|  1274.47
 +
|-
 +
|  MotherProbL1-mi016a
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi016a.dat|mi016a.dat]]
 +
|  16x16
 +
|  1148.71
 +
|-
 +
|  MotherProbL1-mi016b
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi016b.dat|mi016b.dat]]
 +
|  16x16
 +
|  1148.55
 +
|-
 +
|  MotherProbL1-mi032a
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi032a.dat|mi032a.dat]]
 +
|  32x32
 +
|  1087.18
 +
|-
 +
|  MotherProbL1-mi032b
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi032b.dat|mi032b.dat]]
 +
|  32x32
 +
|  1087.07
 +
|-
 +
|  MotherProbL1-mi032c
 +
| [[Media:MotherProbL1-mi.mod|MotherProbL1-mi.mod]]
 +
| [[Media:mi032c.dat|mi032c.dat]]
 +
|  32x32
 +
|  1087.12
 +
|-
 +
|  MotherProbL2-md008
 +
| [[Media:MotherProbL2.mod|MotherProbL2.mod]]
 +
| [[Media:md008.dat|md008.dat]]
 +
|  8x8
 +
|  1274.4697
 +
|-
 +
|  MotherProbL2-md016
 +
| [[Media:MotherProbL2.mod|MotherProbL2.mod]]
 +
| [[Media:md016.dat|md016.dat]]
 +
|  16x16
 +
|  1148.5152
 +
|-
 +
|  MotherProbL2-md032
 +
| [[Media:MotherProbL2.mod|MotherProbL2.mod]]
 +
| [[Media:md032.dat|md032.dat]]
 +
|  32x32
 +
|  1087.0657 (?)
 +
|-
 +
|  MotherProbL2-mi008a
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi008a.dat|mi008a.dat]]
 +
|  8x8
 +
|  1274.47
 +
|-
 +
|  MotherProbL2-mi016a
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi016a.dat|mi016a.dat]]
 +
|  16x16
 +
|  1148.71
 +
|-
 +
|  MotherProbL2-mi016b
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi016b.dat|mi016b.dat]]
 +
|  16x16
 +
|  1148.55
 +
|-
 +
|  MotherProbL2-mi032a
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi032a.dat|mi032a.dat]]
 +
|  32x32
 +
|  1087.18
 +
|-
 +
|  MotherProbL2-mi032b
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi032b.dat|mi032b.dat]]
 +
|  32x32
 +
|  1087.07
 +
|-
 +
|  MotherProbL2-mi032c
 +
| [[Media:MotherProbL2-mi.mod|MotherProbL2-mi.mod]]
 +
| [[Media:mi032c.dat|mi032c.dat]]
 +
|  32x32
 +
|  1087.12
 +
|-
 +
|+ align="bottom" | MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial 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.
 
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.
Line 53: Line 322:
 
|  Crank-Nicolson formula
 
|  Crank-Nicolson formula
 
|}
 
|}
 +
 +
  
 
{| border="1" cellpadding="1" cellspacing="1"
 
{| border="1" cellpadding="1" cellspacing="1"
Line 64: Line 335:
 
|  RobinBin-08  
 
|  RobinBin-08  
 
| [[Media:RobinBin.mod|RobinBin.mod]]
 
| [[Media:RobinBin.mod|RobinBin.mod]]
−
| [[Media:RobinOneD-08.dat|RobinOneD-08.dat]]
+
| [[Media:m08.dat|m08.dat]]
 
|  8x8
 
|  8x8
 
|  0.0305
 
|  0.0305
Line 70: Line 341:
 
|  RobinBin-16  
 
|  RobinBin-16  
 
| [[Media:RobinBin.mod|RobinBin.mod]]
 
| [[Media:RobinBin.mod|RobinBin.mod]]
−
| [[Media:RobinOneD-16.dat|RobinOneD-16.dat]]
+
| [[Media:m16.dat|m16.dat]]
 
|  16x16
 
|  16x16
 
|  0.0190
 
|  0.0190
Line 76: Line 347:
 
|  RobinBin-32  
 
|  RobinBin-32  
 
| [[Media:RobinBin.mod|RobinBin.mod]]
 
| [[Media:RobinBin.mod|RobinBin.mod]]
−
| [[Media:RobinOneD-32.dat|RobinOneD-32.dat]]
+
| [[Media:m32.dat|m32.dat]]
 
|  32x32
 
|  32x32
 
|  0.0145
 
|  0.0145
Line 82: Line 353:
 
|  RobinBinL1-08  
 
|  RobinBinL1-08  
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
−
| [[Media:RobinOneD-08.dat|RobinOneD-08.dat]]
+
| [[Media:m08.dat|m08.dat]]
 
|  8x8
 
|  8x8
 
|  0.0305
 
|  0.0305
Line 88: Line 359:
 
|  RobinBinL1-16  
 
|  RobinBinL1-16  
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
−
| [[Media:RobinOneD-16.dat|RobinOneD-16.dat]]
+
| [[Media:m16.dat|m16.dat]]
 
|  16x16
 
|  16x16
 
|  0.0190
 
|  0.0190
Line 94: Line 365:
 
|  RobinBinL1-32  
 
|  RobinBinL1-32  
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
 
| [[Media:RobinBinL1.mod|RobinBinL1.mod]]
−
| [[Media:RobinOneD-32.dat|RobinOneD-32.dat]]
+
| [[Media:m32.dat|m32.dat]]
 
|  32x32
 
|  32x32
 
|  0.0145
 
|  0.0145
Line 100: Line 371:
 
|  RobinInt-08  
 
|  RobinInt-08  
 
| [[Media:RobinInt.mod|RobinInt.mod]]
 
| [[Media:RobinInt.mod|RobinInt.mod]]
−
| [[Media:RobinOneD-08.dat|RobinOneD-08.dat]]
+
| [[Media:m08.dat|m08.dat]]
 
|  8x8
 
|  8x8
 
|  0.0305
 
|  0.0305
Line 106: Line 377:
 
|  RobinInt-16  
 
|  RobinInt-16  
 
| [[Media:RobinInt.mod|RobinInt.mod]]
 
| [[Media:RobinInt.mod|RobinInt.mod]]
−
| [[Media:RobinOneD-16.dat|RobinOneD-16.dat]]
+
| [[Media:m16.dat|m16.dat]]
 
|  16x16
 
|  16x16
 
|  0.0190
 
|  0.0190
Line 112: Line 383:
 
|  RobinInt-32  
 
|  RobinInt-32  
 
| [[Media:RobinInt.mod|RobinInt.mod]]
 
| [[Media:RobinInt.mod|RobinInt.mod]]
−
| [[Media:RobinOneD-32.dat|RobinOneD-32.dat]]
+
| [[Media:m32.dat|m32.dat]]
 
|  32x32
 
|  32x32
 
|  0.0145
 
|  0.0145
Line 118: Line 389:
 
|  RobinIntL1-08  
 
|  RobinIntL1-08  
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
−
| [[Media:RobinOneD-08.dat|RobinOneD-08.dat]]
+
| [[Media:m08.dat|m08.dat]]
 
|  8x8
 
|  8x8
 
|  0.0305
 
|  0.0305
Line 124: Line 395:
 
|  RobinIntL1-16  
 
|  RobinIntL1-16  
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
−
| [[Media:RobinOneD-16.dat|RobinOneD-16.dat]]
+
| [[Media:m16.dat|m16.dat]]
 
|  16x16
 
|  16x16
 
|  0.0190
 
|  0.0190
Line 130: Line 401:
 
|  RobinIntL1-32  
 
|  RobinIntL1-32  
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
 
| [[Media:RobinIntL1.mod|RobinIntL1.mod]]
−
| [[Media:RobinOneD-32.dat|RobinOneD-32.dat]]
+
| [[Media:m32.dat|m32.dat]]
 
|  32x32
 
|  32x32
 
|  0.0145
 
|  0.0145
Line 137: Line 408:
 
|}
 
|}
  
−
=== Parabolic Robin Boundary Problem in Two Spatial Dimensions ===
+
= Parabolic Robin Boundary Problem in Two Spatial Dimensions =
−
 
 
−
 
 
−
=== Heat Equation Actuator-Placement ===
 
  
 +
= Heat Equation Actuator-Placement =
  
−
=== Subsurface Flow Well-Placement ===
+
= Subsurface Flow Well-Placement =

Latest revision as of 16:21, 24 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


NAME mod file dat file mesh optimal objective
SrcDetct-MeshDep-008-1 SrcDetct.mod MeshDep-008-1.dat 8x8 0.0022
SrcDetct-MeshDep-008-2 SrcDetct.mod MeshDep-008-2.dat 8x8 0.0001
SrcDetct-MeshDep-008-3 SrcDetct.mod MeshDep-008-3.dat 8x8 0.0001
SrcDetct-MeshDep-016-1 SrcDetct.mod MeshDep-016-1.dat 16x16 0.0076
SrcDetct-MeshDep-016-2 SrcDetct.mod MeshDep-016-2.dat 16x16 0.0000
SrcDetct-MeshDep-016-3 SrcDetct.mod MeshDep-016-3.dat 16x16 0.5675
SrcDetct-MeshDep-032-1 SrcDetct.mod MeshDep-032-1.dat 32x32 0.0298
SrcDetct-MeshDep-032-2 SrcDetct.mod MeshDep-032-2.dat 32x32 0.0000
SrcDetct-MeshDep-032-3 SrcDetct.mod MeshDep-032-3.dat 32x32 2.2180
SrcDetct-MeshInd-008-1 SrcDetct.mod MeshInd-008-1.dat 8x8 0.0002
SrcDetct-MeshInd-008-2 SrcDetct.mod MeshInd-008-2.dat 8x8 0.0001
SrcDetct-MeshInd-008-3 SrcDetct.mod MeshInd-008-3.dat 8x8 0.0001
SrcDetct-MeshInd-016-1 SrcDetct.mod MeshInd-016-1.dat 16x16 0.0006
SrcDetct-MeshInd-016-2 SrcDetct.mod MeshInd-016-2.dat 16x16 0.0004
SrcDetct-MeshInd-016-3 SrcDetct.mod MeshInd-016-3.dat 16x16 0.3271
SrcDetct-MeshInd-032-1 SrcDetct.mod MeshInd-032-1.dat 32x32 0.0023
SrcDetct-MeshInd-032-2 SrcDetct.mod MeshInd-032-2.dat 32x32 0.0015
SrcDetct-MeshInd-032-3 SrcDetct.mod MeshInd-032-3.dat 32x32 1.3068
MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension


In this problem, the state variables, u, can be eliminated, resulting in a pure integer QP. The model that defines the problems without state variables is SrcDetctElim.mod, and the AMPL script, Presolve.ampl implements the presolve step. The calling sequence is

ampl: model SrcDetctElim.mod; data MeshDep-008-1.dat; include Presolve.ampl;

for the small example, SrcDetct-MeshDep-008-1.

The Mother Problem: Distributed Control with Neumann Boundary Conditions

The objective is to find optimal control and state variables for an optimal control problem that has Poisson equation with a potential term and Neumann boundary conditions. Control variables are treated as binary variables.

Source: Continuous form taken from OPTPDE library Problem ccdist1 submitted by Roland Herzog, see http://www.optpde.uni-hamburg.de/result.php?id=2

Type of PDE Poisson equation with a potential term on [01]x[0,1] with 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 Five-point finite-difference stencil


NAME mod file dat file mesh optimal objective
MotherProbL1-md008 MotherProbL1.mod md008.dat 8x8 1274.4697
MotherProbL1-md016 MotherProbL1.mod md016.dat 16x16 1148.5152
MotherProbL1-md032 MotherProbL1.mod md032.dat 32x32 1087.0657
MotherProbL1-mi008a MotherProbL1-mi.mod mi008a.dat 8x8 1274.47
MotherProbL1-mi016a MotherProbL1-mi.mod mi016a.dat 16x16 1148.71
MotherProbL1-mi016b MotherProbL1-mi.mod mi016b.dat 16x16 1148.55
MotherProbL1-mi032a MotherProbL1-mi.mod mi032a.dat 32x32 1087.18
MotherProbL1-mi032b MotherProbL1-mi.mod mi032b.dat 32x32 1087.07
MotherProbL1-mi032c MotherProbL1-mi.mod mi032c.dat 32x32 1087.12
MotherProbL2-md008 MotherProbL2.mod md008.dat 8x8 1274.4697
MotherProbL2-md016 MotherProbL2.mod md016.dat 16x16 1148.5152
MotherProbL2-md032 MotherProbL2.mod md032.dat 32x32 1087.0657 (?)
MotherProbL2-mi008a MotherProbL2-mi.mod mi008a.dat 8x8 1274.47
MotherProbL2-mi016a MotherProbL2-mi.mod mi016a.dat 16x16 1148.71
MotherProbL2-mi016b MotherProbL2-mi.mod mi016b.dat 16x16 1148.55
MotherProbL2-mi032a MotherProbL2-mi.mod mi032a.dat 32x32 1087.18
MotherProbL2-mi032b MotherProbL2-mi.mod mi032b.dat 32x32 1087.07
MotherProbL2-mi032c MotherProbL2-mi.mod mi032c.dat 32x32 1087.12
MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial 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.

Type of PDE Heat equation on [0,1]x[0,1.58] with Robin 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


NAME mod file dat file mesh optimal objective
RobinBin-08 RobinBin.mod m08.dat 8x8 0.0305
RobinBin-16 RobinBin.mod m16.dat 16x16 0.0190
RobinBin-32 RobinBin.mod m32.dat 32x32 0.0145
RobinBinL1-08 RobinBinL1.mod m08.dat 8x8 0.0305
RobinBinL1-16 RobinBinL1.mod m16.dat 16x16 0.0190
RobinBinL1-32 RobinBinL1.mod m32.dat 32x32 0.0145
RobinInt-08 RobinInt.mod m08.dat 8x8 0.0305
RobinInt-16 RobinInt.mod m16.dat 16x16 0.0190
RobinInt-32 RobinInt.mod m32.dat 32x32 0.0145
RobinIntL1-08 RobinIntL1.mod m08.dat 8x8 0.0305
RobinIntL1-16 RobinIntL1.mod m16.dat 16x16 0.0190
RobinIntL1-32 RobinIntL1.mod m32.dat 32x32 0.0145
MIPDECOlib: Parabolic Robin Boundary Problem in One Spatial Dimension

Parabolic Robin Boundary Problem in Two Spatial Dimensions

Heat Equation Actuator-Placement

Subsurface Flow Well-Placement

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