quadratic_program.h

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// Copyright 2010-2021 Google LLC
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
//     http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
 
#ifndef PDLP_QUADRATIC_PROGRAM_H_
#define PDLP_QUADRATIC_PROGRAM_H_
 
#include <cstdint>
#include <limits>
#include <optional>
#include <string>
#include <utility>
#include <vector>
 
#include "Eigen/Core"
#include "Eigen/SparseCore"
#include "absl/status/status.h"
#include "absl/status/statusor.h"
#include "absl/types/optional.h"
#include "ortools/base/logging.h"
#include "ortools/linear_solver/linear_solver.pb.h"
 
namespace operations_research::pdlp {
 
// 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 symmetric and positive semi-definite.
//
// For convenience, the struct also stores a 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.
struct QuadraticProgram {
  QuadraticProgram(int64_t num_variables, int64_t num_constraints) {
    ResizeAndInitialize(num_variables, num_constraints);
  }
  QuadraticProgram() : QuadraticProgram(0, 0) {}
 
  // QuadraticPrograms may be copied or moved. Eigen::SparseMatrix doesn't
  // have move operations so we use custom implementations based on swap.
  QuadraticProgram(const QuadraticProgram& other) = default;
  QuadraticProgram(QuadraticProgram&& other) noexcept
      : objective_vector(std::move(other.objective_vector)),
        objective_matrix(std::move(other.objective_matrix)),
        constraint_lower_bounds(std::move(other.constraint_lower_bounds)),
        constraint_upper_bounds(std::move(other.constraint_upper_bounds)),
        variable_lower_bounds(std::move(other.variable_lower_bounds)),
        variable_upper_bounds(std::move(other.variable_upper_bounds)),
        problem_name(std::move(other.problem_name)),
        variable_names(std::move(other.variable_names)),
        constraint_names(std::move(other.constraint_names)),
        objective_offset(other.objective_offset),
        objective_scaling_factor(other.objective_scaling_factor) {
    constraint_matrix.swap(other.constraint_matrix);
  }
  QuadraticProgram& operator=(const QuadraticProgram& other) = default;
  QuadraticProgram& operator=(QuadraticProgram&& other) {
    objective_vector = std::move(other.objective_vector);
    objective_matrix = std::move(other.objective_matrix);
    constraint_matrix.swap(other.constraint_matrix);
    constraint_lower_bounds = std::move(other.constraint_lower_bounds);
    constraint_upper_bounds = std::move(other.constraint_upper_bounds);
    variable_lower_bounds = std::move(other.variable_lower_bounds);
    variable_upper_bounds = std::move(other.variable_upper_bounds);
    problem_name = std::move(other.problem_name);
    variable_names = std::move(other.variable_names);
    constraint_names = std::move(other.constraint_names);
    objective_offset = other.objective_offset;
    objective_scaling_factor = other.objective_scaling_factor;
    return *this;
  }
 
  // Initializes the quadratic program with num_variables variables and
  // num_constraints constraints. Lower and upper bounds are set to to negative
  // and positive infinity, repectively. The 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.
  void ResizeAndInitialize(int64_t num_variables, int64_t num_constraints) {
    constexpr double kInfinity = std::numeric_limits<double>::infinity();
    objective_vector = Eigen::VectorXd::Zero(num_variables);
    objective_matrix.reset();
    constraint_matrix.resize(num_constraints, num_variables);
    constraint_lower_bounds =
        Eigen::VectorXd::Constant(num_constraints, -kInfinity);
    constraint_upper_bounds =
        Eigen::VectorXd::Constant(num_constraints, kInfinity);
    variable_lower_bounds =
        Eigen::VectorXd::Constant(num_variables, -kInfinity);
    variable_upper_bounds = Eigen::VectorXd::Constant(num_variables, kInfinity);
    problem_name.reset();
    variable_names.reset();
    constraint_names.reset();
    objective_offset = 0.0;
    objective_scaling_factor = 1.0;
  }
 
  // Returns objective_scaling_factor * (objective + objective_offset).
  // objective_scaling_factor is useful for modeling maximization problems.
  // For example, max c'x = -1 * min (-c)'x. objective_offset can be a
  // by-product of presolve transformations that eliminate variables.
  double ApplyObjectiveScalingAndOffset(double objective) const {
    return objective_scaling_factor * (objective + objective_offset);
  }
 
  Eigen::VectorXd objective_vector;
  // If this field isn't set, the objective matrix is interpreted to be zero,
  // i.e., this is a linear programming problem.
  std::optional<Eigen::DiagonalMatrix<double, Eigen::Dynamic>> objective_matrix;
  Eigen::SparseMatrix<double, Eigen::ColMajor, int64_t> constraint_matrix;
  Eigen::VectorXd constraint_lower_bounds, constraint_upper_bounds;
  Eigen::VectorXd variable_lower_bounds, variable_upper_bounds;
  // The problem, constraint, and variable names are optional.
  absl::optional<std::string> problem_name;
  absl::optional<std::vector<std::string>> variable_names;
  absl::optional<std::vector<std::string>> constraint_names;
 
  // These fields are provided for convenience; they don't change the
  // mathematical definition of the problem, but they could change the objective
  // values reported to the user.
  double objective_offset;
  double objective_scaling_factor;
};
 
// Returns InvalidArgument if vector or matrix dimensions are inconsistent.
// Returns OkStatus otherwise.
absl::Status ValidateQuadraticProgramDimensions(const QuadraticProgram& qp);
 
inline bool IsLinearProgram(const QuadraticProgram& qp) {
  return !qp.objective_matrix.has_value();
}
 
// Checks if the lower and upper bounds of the problem are consistent, i.e. for
// each variable and constraint bound we have lower_bound <= upper_bound. If
// the input is consistent the method returns true, otherwise it returns false.
// See also HasValidBounds(const ShardedQuadraticProgram&).
bool HasValidBounds(const QuadraticProgram& qp);
 
// Converts an MPModelProto into a QuadraticProgram.
// Returns an error if general constraints are present.
// If relax_integer_variables is true integer variables are relaxed to
// continuous; otherwise integer variables are an error.
// If include_names is true (the default is false), the problem, constraint,
// and variable names are included in the QuadraticProgram; otherwise they are
// left empty.
// Maximization problems are converted to minimization by negating the
// objective and setting objective_scaling_factor to -1, which preserves the
// reported objective values.
absl::StatusOr<QuadraticProgram> QpFromMpModelProto(
    const MPModelProto& proto, bool relax_integer_variables,
    bool include_names = false);
 
// Returns InvalidArgument if the given quadratic program is too large to
// convert to MPModelProto and OkStatus otherwise.
absl::Status CanFitInMpModelProto(const QuadraticProgram& qp);
 
// Converts a QuadraticProgram into an MPModelProto. To preserve objective
// values in the conversion, the objective vector, objective matrix, and
// objective offset are scaled by objective_scaling_factor, and if
// objective_scaling_factor is negative, then the proto is a maximization
// problem (otherwise it's a minimization problem). Returns InvalidArgumentError
// if objective_scaling_factor is zero or if CanFitInMpModelProto() fails.
absl::StatusOr<MPModelProto> QpToMpModelProto(const QuadraticProgram& qp);
 
// Like matrix.setFromTriplets(triplets), except that setFromTriplets results
// in having three copies of the nonzeros in memory at the same time, because it
// first fills one matrix from triplets, and then transposes it into another.
// This avoids having the third copy in memory by sorting the triplets,
// reserving space in the matrix, and then inserting in sorted order.
// Compresses the matrix (SparseMatrix.makeCompressed()) after loading it.
// NOTE: This intentionally passes triplets by copy, because it modifies them.
// To avoid the copy, pass a move reference.
void SetEigenMatrixFromTriplets(
    std::vector<Eigen::Triplet<double, int64_t>> triplets,
    Eigen::SparseMatrix<double, Eigen::ColMajor, int64_t>& matrix);
 
// Utility functions for internal use only.
namespace internal {
// Like CanFitInMpModelProto() but has an extra argument for the largest number
// of variables, constraints, or objective non-zeros that should be counted as
// convertible. CanFitInMpModelProto() passes 2^31 - 1 for this argument and
// unit tests pass small values.
absl::Status TestableCanFitInMpModelProto(const QuadraticProgram& qp,
                                          int64_t largest_ok_size);
 
// Modifies a vector of Eigen::Triplets in place, combining consecutive entries
// with the same row and column, summing their values.  This is most effective
// if the triplets are sorted by row and column, so that multiple entries for
// the same entry will be consecutive.
void CombineRepeatedTripletsInPlace(
    std::vector<Eigen::Triplet<double, int64_t>>& triplets);
}  // namespace internal
}  // namespace operations_research::pdlp
 
#endif  // PDLP_QUADRATIC_PROGRAM_H_