Pipal Namespace Reference

Namespace for the Pipal library. More...

Classes
struct	Acceptance
	Class for managing the acceptance criteria of the solver. More...
struct	Direction
	Class for managing the current search direction of the solver. More...
struct	Input
	Input structure holding all the data defining the optimization problem. More...
struct	Iterate
	Class for managing the current iterate of the solver. More...
class	Output
	Pretty-printing and timing utilities for solver output. More...
struct	Parameter
	Internal parameters for the solver algorithm. More...
class	Problem
	Problem class for the Pipal library. More...
class	ProblemWrapper
	Wrapper class for the Problem class. More...
class	Solver
	Solver class for the Pipal library. More...

Typedefs
using	Integer = PIPAL_DEFAULT_INTEGER_TYPE
	The Integer type as used for the API.
template<typename Real>
using	Vector = Eigen::Vector<Real, Eigen::Dynamic>
template<typename Real>
using	Matrix = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>
template<typename Real>
using	SparseMatrix = Eigen::SparseMatrix<Real>
template<typename Real>
using	Array = Eigen::Array<Real, Eigen::Dynamic, 1>
using	Indices = Eigen::Array<Integer, Eigen::Dynamic, 1>
using	Mask = Eigen::Array<bool, Eigen::Dynamic, 1>
using	Algorithm = enum class Algorithm : Integer {CONSERVATIVE = 0, ADAPTIVE = 1}
	Enumeration for the algorithm choice.
using	Counter
	Internal counters for solver statistics.

Functions
static Indices	find (Mask const &mask)
	Select elements from a vector based on a boolean mask.
template<typename Real>
static void	insert_block (SparseMatrix< Real > &mat, SparseMatrix< Real > const &blk, Integer const row_offset, Integer const col_offset)
	Insert a sparse block into a sparse matrix at the specified offsets.
template<typename Real>
static void	insert_block (SparseMatrix< Real > &mat, SparseMatrix< Real > const &blk, Indices const row_index, Indices const col_index, Integer const row_offset, Integer const col_offset)
	Insert a sparse block into a sparse matrix at the specified offsets.

Detailed Description

Penalty-interior-point algorithm (Pipal) is a library for nonlinear constrained optimization with inequality constraints (it does not explicitly handle equality constraints). Precisely speaking, it will compute the solution to the optimization problem

\[ \begin{array}{l} \text{minimize} ~ f(\mathbf{x}) \\ \text{subject to} ~ \mathbf{c}(\mathbf{x}) \leq \mathbf{0} \end{array} \text{,} \]

where \(\mathbf{x} \in \mathbb{R}^n\) is the vector of optimization variables, \(f: \mathbb{R}^n \to \mathbb{R}\) is the objective function, and \(\mathbf{c}: \mathbb{R}^n \to \mathbb{R}^m\) are the constraints.

Note

To create an equality constraint \( h(\mathbf{x}) = 0 \), one can define two inequality constraints \( h(\mathbf{x}) \leq 0 \) and \( -h(\mathbf{x}) \leq 0 \).

This code is mostly based on the descriptions provided in this reference:

• Frank E. Curtis. A penalty-interior-point algorithm for nonlinear constrained optimization. Mathematical Programming Computation (2012) 4:181-209. DOI: 10.1007/s12532-012-0041-4.

Typedef Documentation

Algorithm

using Pipal::Algorithm = enum class Algorithm : Integer {CONSERVATIVE = 0, ADAPTIVE = 1}

The Algorithm enumeration defines the possible algorithm choices for the solver. The options are CONSERVATIVE and ADAPTIVE.

Array

template<typename Real>

using Pipal::Array = Eigen::Array<Real, Eigen::Dynamic, 1>

Counter

using Pipal::Counter

Initial value:

 struct Counter
  {
    Integer f{0}; 
    Integer g{0}; 
    Integer H{0}; 
    Integer k{0}; 
    Integer M{0}; 
 
    
    Counter() = default;
 
    
    Counter(Counter const &) = delete;
 
    
    Counter & operator=(Counter const &) = delete;
 
  }

Indices

using Pipal::Indices = Eigen::Array<Integer, Eigen::Dynamic, 1>

Integer

using Pipal::Integer = PIPAL_DEFAULT_INTEGER_TYPE

The Integer type, #define the preprocessor symbol PIPAL_DEFAULT_INTEGER_TYPE. The default value is int.

Mask

using Pipal::Mask = Eigen::Array<bool, Eigen::Dynamic, 1>

Matrix

template<typename Real>

using Pipal::Matrix = Eigen::Matrix<Real, Eigen::Dynamic, Eigen::Dynamic>

SparseMatrix

template<typename Real>

using Pipal::SparseMatrix = Eigen::SparseMatrix<Real>

Vector

template<typename Real>

using Pipal::Vector = Eigen::Vector<Real, Eigen::Dynamic>

Function Documentation

find()

Indices Pipal::find ( Mask const & mask )

static

Parameters

[in]

mask

The boolean mask.

Returns

The selected elements from the input vector.

insert_block() [1/2]

template<typename Real>

void Pipal::insert_block ( SparseMatrix< Real > & mat, SparseMatrix< Real > const & blk, Indices const row_index, Indices const col_index, Integer const row_offset, Integer const col_offset )

static

Template Parameters

Real	Floating-point type used by the algorithm.
CheckZero	Whether to skip zero entries when inserting.

Parameters

[in,out]	mat	Sparse matrix where to insert the block.
[in]	blk	Sparse matrix block to insert.
[in]	row_index	Row indices in the block matrix.
[in]	col_index	Column indices in the block matrix.
[in]	row_offset	Row offset in the sparse matrix.
[in]	col_offset	Column offset in the sparse matrix.

insert_block() [2/2]

template<typename Real>

void Pipal::insert_block ( SparseMatrix< Real > & mat, SparseMatrix< Real > const & blk, Integer const row_offset, Integer const col_offset )

static

Template Parameters

Real	Floating-point type used by the algorithm.
CheckZero	Whether to skip zero entries when inserting.

Parameters

[in,out]	mat	Sparse matrix where to insert the block.
[in]	blk	Sparse matrix block to insert.
[in]	row_offset	Row offset in the sparse matrix.
[in]	col_offset	Column offset in the sparse matrix.