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Ipopt Documentation
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Ipopt Documentation
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Pure Primal Dual System Solver Base Class. More...
#include <IpPDSystemSolver.hpp>
Inheritance diagram for Ipopt::PDSystemSolver:Private Member Functions | |
Default Compiler Generated Methods | |
(Hidden to avoid implicit creation/calling). These methods are not implemented and we do not want the compiler to implement them for us, so we declare them private and do not define them. This ensures that they will not be implicitly created/called. | |
| PDSystemSolver & | operator= (const PDSystemSolver &) |
| Default Assignment Operator. | |
Additional Inherited Members | |
| Protected Member Functions inherited from Ipopt::AlgorithmStrategyObject | |
| const Journalist & | Jnlst () const |
| IpoptNLP & | IpNLP () const |
| IpoptData & | IpData () const |
| IpoptCalculatedQuantities & | IpCq () const |
| bool | HaveIpData () const |
Pure Primal Dual System Solver Base Class.
This is the base class for all derived Primal-Dual System Solver Types.
Here, we understand the primal-dual system as the following linear system:
\( \left[\begin{array}{cccccccc} W & 0 & J_c^T & J_d^T & -P^x_L & P^x_U & 0 & 0 \\ 0 & 0 & 0 & -I & 0 & 0 & -P_L^d & P_U^d \\ J_c & 0 & 0 & 0 & 0 & 0 & 0 & 0\\ J_d & -I & 0 & 0 & 0 & 0 & 0 & 0\\ Z_L(P_L^x)^T & 0 & 0 & 0 & Sl^x_L & 0 & 0 & 0\\ -Z_U(P_U^x)^T & 0 & 0 & 0 & 0 & Sl^x_U & 0 & 0\\ 0 & V_L(P_L^d)^T & 0 & 0 & 0 & 0 & Sl^s_L & 0 \\ 0 & -V_U(P_U^d)^T & 0 & 0 & 0 & 0 & 0 & Sl^s_U \\ \end{array}\right] \left(\begin{array}{c} sol_x\\ sol_s\\ sol_c\\ sol_d\\ sol^z_L\\ sol^z_U\\ sol^v_L\\ sol^v_U \end{array}\right) = \left(\begin{array}{c} rhs_x\\ rhs_s\\ rhs_c\\ rhs_d\\ rhs^z_L\\ rhs^z_U\\ rhs^v_L\\ rhs^v_U \end{array}\right) \)
Here, \(Sl^x_L = (P^x_L)^T x - x_L\), \(Sl^x_U = x_U - (P^x_U)^T x\), \(Sl^d_L = (P^d_L)^T d(x) - d_L\), \(Sl^d_U = d_U - (P^d_U)^T d(x)\). The results returned to the caller is \(res = \alpha * sol + \beta * res\).
The solution of this linear system (in order to compute the search direction of the algorithm) usually requires a considerable amount of computation time. Therefore, it is important to tailor the solution of this system to the characteristics of the problem. The purpose of this base class is to provide a generic interface to the algorithm that it can use whenever it requires a solution of the above system. Particular implementation can then be written to provide the methods defined here.
It is implicitly assumed here, that the upper left 2 by 2 block is possibly modified (implicitly or explicitly) so that its projection onto the null space of the overall constraint Jacobian \(\left[\begin{array}{cc}J_c & 0\\J_d & -I\end{array}\right]\) is positive definite. This is necessary to guarantee certain descent properties of the resulting search direction. For example, in the full space implementation, a multiple of the identity might be added to the upper left 2 by 2 block.
Note that the Solve method might be called several times for different right hand sides, but with identical data. Therefore, if possible, an implementation of PDSystem should check whether the incoming data has changed, and not redo factorization etc. unless necessary.
Definition at line 74 of file IpPDSystemSolver.hpp.
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inline |
Default Constructor.
Definition at line 80 of file IpPDSystemSolver.hpp.
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inlinevirtual |
Destructor.
Definition at line 84 of file IpPDSystemSolver.hpp.
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pure virtual |
overloaded from AlgorithmStrategyObject
Implements Ipopt::AlgorithmStrategyObject.
Implemented in Ipopt::PDFullSpaceSolver.
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pure virtual |
Solve the primal dual system, given one right hand side.
If the flag allow_inexact is set to true, it is not necessary to solve the system to best accuracy; for example, we don't want iterative refinement during the computation of the second order correction. On the other hand, if improve_solution is true, the solution given in res should be improved (here beta has to be zero, and res is assume to be the solution for the system using rhs, without the factor alpha...).
Implemented in Ipopt::PDFullSpaceSolver.
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private |
Default Assignment Operator.
