Functional Interface

ROL's functional interface. More...

Classes
class	ROL::Objective< Real >
	Provides the interface to evaluate objective functions. More...
class	ROL::BoundConstraint< Real >
	Provides the interface to apply upper and lower bound constraints. More...
class	ROL::EqualityConstraint< Real >
	Defines the equality constraint operator interface. More...
class	ROL::Objective_SimOpt< Real >
	Provides the interface to evaluate simulation-based objective functions. More...
class	ROL::EqualityConstraint_SimOpt< Real >
	Defines the equality constraint operator interface for simulation-based optimization. More...
class	ROL::BlockOperator< Real >
	Provides the interface to apply a block operator to a partitioned vector. More...
class	ROL::BlockOperator2< Real >
	Provides the interface to apply a 2x2 block operator to a partitioned vector. More...
class	ROL::BlockOperator2Determinant< Real >
	Provides the interface to the block determinant of a 2x2 block operator More...
class	ROL::BlockOperator2Diagonal< Real >
	Provides the interface to apply a 2x2 block diagonal operator to a partitioned vector. More...
class	ROL::BlockOperator2UnitLower< Real >
	Provides the interface to apply a 2x2 block unit lower operator to a partitioned vector. More...
class	ROL::BlockOperator2UnitUpper< Real >
	Provides the interface to apply a 2x2 block unit upper operator to a partitioned vector. More...
class	ROL::DiagonalOperator< Real >
	Provides the interface to apply a diagonal operator which acts like elementwise multiplication when apply() is used and elementwise division when applyInverse() is used. More...
class	ROL::DyadicOperator< Real >
	Interface to apply a dyadic operator to a vector. More...
class	ROL::HouseholderReflector< Real >
	Provides the interface to create a Householder reflector operator, that when applied to a vector x, produces a vector parallel to y. More...
class	ROL::IdentityOperator< Real >
	Multiplication by unity. More...
class	ROL::LinearOperator< Real >
	Provides the interface to apply a linear operator. More...
class	ROL::LinearOperatorFromEqualityConstraint< Real >
	A simple wrapper which allows application of constraint Jacobians through the LinearOperator interface. More...
class	ROL::LinearOperatorProduct< Real >
	Provides the interface to the sequential application of linear operators. More...
class	ROL::LinearOperatorSum< Real >
	Provides the interface to sum of linear operators applied to a vector More...
class	ROL::NullOperator< Real >
	Multiplication by zero. More...
class	ROL::SchurComplement
	Given a 2x2 block operator, perform the Schur reduction and return the decoupled system components. More...
class	ROL::StdLinearOperator< Real >
	Provides the std::vector implementation to apply a linear operator, which is a std::vector representation of column-stacked matrix. More...
class	ROL::StdLinearOperatorFactory
	Creates StdLinearOperator objects which wrap random matrices of the desired size and property More...
class	ROL::StdTridiagonalOperator< Real >
	Provides the std::vector implementation to apply a linear operator, which encapsulates a tridiagonal matrix. More...
class	ROL::AugmentedLagrangian< Real >
	Provides the interface to evaluate the augmented Lagrangian. More...
class	ROL::AugmentedLagrangian_SimOpt< Real >
	Provides the interface to evaluate the SimOpt augmented Lagrangian. More...
class	ROL::BinaryConstraint< Real >
	Implements an equality constraint function that evaluates to zero on the surface of a bounded parallelpiped and is positive in the interior. More...
class	ROL::BoundConstraint_Partitioned< Real >
	A composite composite BoundConstraint formed from bound constraints on subvectors of a PartitionedVector. More...
class	ROL::BoundInequalityConstraint< Real >
	Provides an implementation for bound inequality constraints. More...
class	ROL::ColemanLiModel< Real >
	Provides the interface to evaluate interior trust-region model functions from the Coleman-Li bound constrained trust-region algorithm. More...
class	ROL::CompositeConstraint< Real >
	Has both inequality and equality constraints. Treat inequality constraint as equality with slack variable. More...
class	ROL::CompositeEqualityConstraint_SimOpt< Real >
	Defines a composite equality constraint operator interface for simulation-based optimization. More...
class	ROL::CompositeObjective< Real >
	Provides the interface to evaluate composite objective functions. More...
class	ROL::CompositeObjective_SimOpt< Real >
	Provides the interface to evaluate simulation-based composite objective functions. More...
class	ROL::EqualityConstraint_Partitioned< Real >
	Allows composition of equality constraints. More...
class	ROL::InequalityConstraint< Real >
	Provides a unique argument for inequality constraints, which otherwise behave exactly as equality constraints. More...
class	ROL::KelleySachsModel< Real >
	Provides the interface to evaluate projected trust-region model functions from the Kelley-Sachs bound constrained trust-region algorithm. More...
class	ROL::LinearEqualityConstraint< Real >
	Provides the interface to evaluate linear equality constraints. More...
class	ROL::LinearObjective< Real >
	Provides the interface to evaluate linear objective functions. More...
class	ROL::LogBarrierObjective< Real >
	Log barrier objective for interior point methods. More...
class	ROL::LowerBoundInequalityConstraint< Real >
	Provides an implementation for lower bound inequality constraints. More...
class	ROL::MoreauYosidaPenalty< Real >
	Provides the interface to evaluate the Moreau-Yosida penalty function. More...
class	ROL::NonlinearLeastSquaresObjective< Real >
	Provides the interface to evaluate nonlinear least squares objective functions. More...
class	ROL::NonlinearLeastSquaresObjective_SimOpt< Real >
	Provides the interface to evaluate nonlinear least squares objective functions. More...
class	ROL::ObjectiveFromBoundConstraint< Real >
	Create a penalty objective from upper and lower bound vectors. More...
class	ROL::ObjectiveMMA< Real >
	Provides the interface to to Method of Moving Asymptotes Objective function. More...
class	ROL::QuadraticObjective< Real >
	Provides the interface to evaluate quadratic objective functions. More...
class	ROL::QuadraticPenalty< Real >
	Provides the interface to evaluate the quadratic constraint penalty. More...
class	ROL::QuadraticPenalty_SimOpt< Real >
	Provides the interface to evaluate the quadratic SimOpt constraint penalty. More...
class	ROL::Reduced_AugmentedLagrangian_SimOpt< Real >
	Provides the interface to evaluate the reduced SimOpt augmented Lagrangian. More...
class	ROL::ScalarLinearEqualityConstraint< Real >
	This equality constraint defines an affine hyperplane. More...
class	ROL::SlacklessObjective< Real >
	This class strips out the slack variables from objective evaluations to create the new objective \( F(x,s) = f(x) \). More...
class	ROL::StdEqualityConstraint< Real >
	Defines the equality constraint operator interface for StdVectors. More...
class	ROL::StdInequalityConstraint< Real >
	Provides a unique argument for inequality constraints using std::vector types, which otherwise behave exactly as equality constraints. More...
class	ROL::StdObjective< Real >
	Specializes the ROL::Objective interface for objective functions that operate on ROL::StdVector's. More...
class	ROL::TrustRegionModel< Real >
	Provides the interface to evaluate trust-region model functions. More...
class	ROL::UpperBoundInequalityConstraint< Real >
	Provides an implementation for upper bound inequality constraints. More...
class	ROL::PenalizedObjective
	Adds barrier term to generic objective. More...
class	ROL::InteriorPoint::CompositeConstraint< Real >
	Has both inequality and equality constraints. Treat inequality constraint as equality with slack variable. More...
class	ROL::InteriorPointPenalty< Real >
	Provides the interface to evaluate the Interior Pointy log barrier penalty function with upper and lower bounds on some elements. More...
class	ROL::InteriorPoint::PrimalDualResidual< Real >
	Express the Primal-Dual Interior Point gradient as an equality constraint. More...
class	ROL::PrimalDualInteriorPointReducedResidual
	Reduced form of the Primal Dual Interior Point residual and the action of its Jacobian. More...
class	ROL::PrimalDualInteriorPointResidual< Real >
	Symmetrized form of the KKT operator for the Type-EB problem with equality and bound multipliers. More...
class	ROL::ParametrizedCompositeObjective< Real >
	Provides the interface to evaluate parametrized composite objective functions. More...
class	ROL::ParametrizedStdObjective< Real >
	Specializes the ROL::Objective interface for objective functions that operate on ROL::StdVector's. More...

Detailed Description

ROL's functional interface.

ROL is used for the numerical solution of smooth optimization problems

\[ \begin{array}{rl} \displaystyle \min_{x} & f(x) \\ \mbox{subject to} & c(x) = 0 \,, \\ & a \le x \le b \,, \end{array} \]

where:

• \(f : \mathcal{X} \rightarrow \mathbb{R}\) is a Fréchet differentiable functional,
• \(c : \mathcal{X} \rightarrow \mathcal{C}\) is a Fréchet differentiable operator,
• \(\mathcal{X}\) and \(\mathcal{C}\) are Banach spaces of functions, and
• \(a \le x \le b\) defines pointwise (componentwise) bounds on \(x\).

This formulation encompasses a variety of useful problem scenarios.

First, the vector spaces \(\mathcal{X}\) and \(\mathcal{C}\), to be defined by the user through the Linear Algebra Interface, can represent real spaces, such as \(\mathcal{X} = \mathbb{R}^n\) and \(\mathcal{C} = \mathbb{R}^m\), and function spaces, such as Hilbert and Banach function spaces. ROL's vector space abstractions enable efficent implementations of general optimization algorithms, spanning traditional nonlinear programming (NLP), optimization with partial differential equation (PDE) or differential algebraic equation (DAE) constraints, and stochastic optimization.

Second, ROL's core methods can solve four types of smooth optimization problems, depending on the structure of the constraints.

• Type-U. No constraints (where \(c(x) = 0\) and \(a \le x \le b\) are absent):

  \[ \begin{array}{rl} \displaystyle \min_{x} & f(x) \end{array} \]

  These problems are known as unconstrained optimization problems. The user implements the methods of the ROL::Objective interface.
• Type-B. Bound constraints (where \(c(x) = 0\) is absent):

  \[ \begin{array}{rl} \displaystyle \min_{x} & f(x) \\ \mbox{subject to} & a \le x \le b \,. \end{array} \]

  This problem is typically handled using projections on active sets or primal-dual active-set methods. ROL provides example implementations of the projections for simple box constraints. Other projections are defined by the user. The user implements the methods of the ROL::BoundConstraint interface.
• Type-E. Equality constraints, generally nonlinear and nonconvex (where \(a \le x \le b\) is absent):

  \[ \begin{array}{rl} \displaystyle \min_{x} & f(x) \\ \mbox{subject to} & c(x) = 0 \,. \end{array} \]

  Equality constraints are handled in ROL using, for example, matrix-free composite-step methods, including sequential quadratic programming (SQP). The user implements the methods of the ROL::EqualityConstraint interface.
• Type-EB. Equality and bound constraints:

  \[ \begin{array}{rl} \displaystyle \min_{x} & f(x) \\ \mbox{subject to} & c(x) = 0 \\ & a \le x \le b \,. \end{array} \]

  This formulation includes general inequality constraints. For example, we can consider the reformulation:

  \[ \begin{array}{rlcccrl} \displaystyle \min_{x} & f(x) &&&& \displaystyle \min_{x,s} & f(x) \\ \mbox{subject to} & c(x) \le 0 & & \quad \longleftrightarrow \quad & & \mbox{subject to} & c(x) + s = 0 \,, \\ &&&&&& s \ge 0 \,. \end{array} \]

  ROL uses a combination of matrix-free composite-step methods, projection methods and primal-dual active set methods to solve these problems. The user implements the methods of the ROL::EqualityConstraint and the ROL::BoundConstraint interfaces.

Third, ROL's design enables streamlined algorithmic extensions, such as the Stochastic Optimization capability.

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