operations_research::pdlp::QuadraticProgram Struct Reference

Detailed Description

Represents the quadratic program (QP): min_x (objective_vector^T x + (1/2) x^T objective_matrix x) s.t. constraint_lower_bounds <= constraint_matrix x <= constraint_upper_bounds variable_lower_bounds <= x <= variable_upper_bounds

constraint_lower_bounds and variable_lower_bounds may include negative infinities. constraint_upper_bounds and variable_upper_bounds may contain positive infinities. Other than that all entries of all fields must be finite. The objective_matrix must be diagonal and non-negative.

variable_lower_bounds, variable_upper_bounds, objective_vector, objective_matrix (if it has a value), and variable_names (if it has a value) must all have the same size as the number of columns in constraint_matrix. constraint_lower_bounds, constraint_upper_bounds, and constraint_names (if it has a value) must all have the same size as the number of rows in constraint_matrix. Consistency of these values is checked by ValidateQuadraticProgramDimensions().

For convenience, the struct also stores scaling_factor and objective_offset. These factors can be used to transform objective values based on the problem definition above into objective values that are meaningful for the user. See ApplyObjectiveScalingAndOffset.

This struct is also intended for use with linear programs (LPs), which are QPs with a zero objective_matrix.

The dual is documented at https://developers.google.com/optimization/lp/pdlp_math.

Definition at line 61 of file quadratic_program.h.

#include <quadratic_program.h>

Public Member Functions
	QuadraticProgram (int64_t num_variables, int64_t num_constraints)
	QuadraticProgram ()
	QuadraticProgram (const QuadraticProgram &other)=default
	QuadraticProgram (QuadraticProgram &&other) noexcept
QuadraticProgram &	operator= (const QuadraticProgram &other)=default
QuadraticProgram &	operator= (QuadraticProgram &&other)
void	ResizeAndInitialize (int64_t num_variables, int64_t num_constraints)
double	ApplyObjectiveScalingAndOffset (double objective) const

Public Attributes
Eigen::VectorXd	objective_vector
std::optional< Eigen::DiagonalMatrix< double, Eigen::Dynamic > >	objective_matrix
Eigen::SparseMatrix< double, Eigen::ColMajor, int64_t >	constraint_matrix
Eigen::VectorXd	constraint_lower_bounds
Eigen::VectorXd	constraint_upper_bounds
Eigen::VectorXd	variable_lower_bounds
Eigen::VectorXd	variable_upper_bounds
std::optional< std::string >	problem_name
std::optional< std::vector< std::string > >	variable_names
std::optional< std::vector< std::string > >	constraint_names
double	objective_offset
double	objective_scaling_factor

Constructor & Destructor Documentation

QuadraticProgram() [1/4]

operations_research::pdlp::QuadraticProgram::QuadraticProgram ( int64_t num_variables, int64_t num_constraints )

inline

Definition at line 62 of file quadratic_program.h.

QuadraticProgram() [2/4]

operations_research::pdlp::QuadraticProgram::QuadraticProgram ( )

inline

Definition at line 65 of file quadratic_program.h.

QuadraticProgram() [3/4]

operations_research::pdlp::QuadraticProgram::QuadraticProgram ( const QuadraticProgram & other )

default

QuadraticProgram may be copied or moved. Eigen::SparseMatrix doesn't have move operations so we use custom implementations based on swap.

QuadraticProgram() [4/4]

operations_research::pdlp::QuadraticProgram::QuadraticProgram ( QuadraticProgram && other )

inlinenoexcept

Definition at line 70 of file quadratic_program.h.

Member Function Documentation

ApplyObjectiveScalingAndOffset()

double operations_research::pdlp::QuadraticProgram::ApplyObjectiveScalingAndOffset ( double objective ) const

inline

Returns objective_scaling_factor * (objective + objective_offset). objective_scaling_factor is useful for modeling maximization problems. For example, max c^T x = -1 * min (-c)^T x. objective_offset can be a by-product of presolve transformations that eliminate variables.

Definition at line 130 of file quadratic_program.h.

operator=() [1/2]

QuadraticProgram & operations_research::pdlp::QuadraticProgram::operator= ( const QuadraticProgram & other )

default

operator=() [2/2]

QuadraticProgram & operations_research::pdlp::QuadraticProgram::operator= ( QuadraticProgram && other )

inline

Definition at line 85 of file quadratic_program.h.

ResizeAndInitialize()

void operations_research::pdlp::QuadraticProgram::ResizeAndInitialize ( int64_t num_variables, int64_t num_constraints )

inline

Initializes the quadratic program with num_variables variables and num_constraints constraints. Lower and upper bounds are set to negative and positive infinity, respectively. objective_matrix is cleared. All other matrices and vectors are set to zero. Resets the optional names (program_name, variable_names, and constraint_names). objective_offset is set to 0 and objective_scaling_factor is set to 1.

Definition at line 107 of file quadratic_program.h.

Member Data Documentation

constraint_lower_bounds

Eigen::VectorXd operations_research::pdlp::QuadraticProgram::constraint_lower_bounds

Definition at line 139 of file quadratic_program.h.

constraint_matrix

Eigen::SparseMatrix<double, Eigen::ColMajor, int64_t> operations_research::pdlp::QuadraticProgram::constraint_matrix

Definition at line 138 of file quadratic_program.h.

constraint_names

std::optional<std::vector<std::string> > operations_research::pdlp::QuadraticProgram::constraint_names

Definition at line 144 of file quadratic_program.h.

constraint_upper_bounds

Eigen::VectorXd operations_research::pdlp::QuadraticProgram::constraint_upper_bounds

Definition at line 139 of file quadratic_program.h.

objective_matrix

std::optional<Eigen::DiagonalMatrix<double, Eigen::Dynamic> > operations_research::pdlp::QuadraticProgram::objective_matrix

If this field isn't set, the objective matrix is interpreted to be zero, i.e., this is a linear programming problem.

Definition at line 137 of file quadratic_program.h.

objective_offset

double operations_research::pdlp::QuadraticProgram::objective_offset

These fields are provided for convenience; they don't change the mathematical definition of the problem, but they change the objective values reported to the user.

Definition at line 149 of file quadratic_program.h.

objective_scaling_factor

double operations_research::pdlp::QuadraticProgram::objective_scaling_factor

Definition at line 150 of file quadratic_program.h.

objective_vector

Eigen::VectorXd operations_research::pdlp::QuadraticProgram::objective_vector

Definition at line 134 of file quadratic_program.h.

problem_name

std::optional<std::string> operations_research::pdlp::QuadraticProgram::problem_name

Definition at line 142 of file quadratic_program.h.

variable_lower_bounds

Eigen::VectorXd operations_research::pdlp::QuadraticProgram::variable_lower_bounds

Definition at line 140 of file quadratic_program.h.

variable_names

std::optional<std::vector<std::string> > operations_research::pdlp::QuadraticProgram::variable_names

Definition at line 143 of file quadratic_program.h.

variable_upper_bounds

Eigen::VectorXd operations_research::pdlp::QuadraticProgram::variable_upper_bounds

Definition at line 140 of file quadratic_program.h.

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The documentation for this struct was generated from the following file:

• ortools/pdlp/quadratic_program.h