# Middle-End Reductions¶

The reductions listed here are not specific to a back end (solver); they can be applied regardless of whether you wish to target, for example, a quadratic program solver or a conic solver.

## Complex2Real¶

class cvxpy.reductions.complex2real.complex2real.Complex2Real(problem=None)[source]

Lifts complex numbers to a real representation.

accepts(problem) → None[source]

States whether the reduction accepts a problem.

Parameters

problem (Problem) – The problem to check.

Returns

True if the reduction can be applied, False otherwise.

Return type

bool

apply(problem)[source]

Applies the reduction to a problem and returns an equivalent problem.

Parameters

problem (Problem) – The problem to which the reduction will be applied.

Returns

• Problem or dict – An equivalent problem, encoded either as a Problem or a dict.

• InverseData, list or dict – Data needed by the reduction in order to invert this particular application.

invert(solution, inverse_data)[source]

Returns a solution to the original problem given the inverse_data.

Parameters
• solution (Solution) – A solution to a problem that generated the inverse_data.

• inverse_data – The data encoding the original problem.

Returns

A solution to the original problem.

Return type

Solution

## CvxAttr2Constr¶

class cvxpy.reductions.cvx_attr2constr.CvxAttr2Constr(problem=None)[source]

Expand convex variable attributes into constraints.

accepts(problem) → bool[source]

States whether the reduction accepts a problem.

Parameters

problem (Problem) – The problem to check.

Returns

True if the reduction can be applied, False otherwise.

Return type

bool

apply(problem)[source]

Applies the reduction to a problem and returns an equivalent problem.

Parameters

problem (Problem) – The problem to which the reduction will be applied.

Returns

• Problem or dict – An equivalent problem, encoded either as a Problem or a dict.

• InverseData, list or dict – Data needed by the reduction in order to invert this particular application.

invert(solution, inverse_data)[source]

Returns a solution to the original problem given the inverse_data.

Parameters
• solution (Solution) – A solution to a problem that generated the inverse_data.

• inverse_data – The data encoding the original problem.

Returns

A solution to the original problem.

Return type

Solution

## Dgp2Dcp¶

class cvxpy.reductions.dgp2dcp.dgp2dcp.Dgp2Dcp(problem=None)[source]

Bases: cvxpy.reductions.canonicalization.Canonicalization

Reduce DGP problems to DCP problems.

This reduction takes as input a DGP problem and returns an equivalent DCP problem. Because every (generalized) geometric program is a DGP problem, this reduction can be used to convert geometric programs into convex form.

Example

>>> import cvxpy as cp
>>>
>>> x1 = cp.Variable(pos=True)
>>> x2 = cp.Variable(pos=True)
>>> x3 = cp.Variable(pos=True)
>>>
>>> monomial = 3.0 * x_1**0.4 * x_2 ** 0.2 * x_3 ** -1.4
>>> posynomial = monomial + 2.0 * x_1 * x_2
>>> dgp_problem = cp.Problem(cp.Minimize(posynomial), [monomial == 4.0])
>>>
>>> dcp2cone = cvxpy.reductions.Dcp2Cone()
>>> assert not dcp2cone.accepts(dgp_problem)
>>>
>>> gp2dcp = cvxpy.reductions.Dgp2Dcp(dgp_problem)
>>> dcp_problem = gp2dcp.reduce()
>>>
>>> assert dcp2cone.accepts(dcp_problem)
>>> dcp_probem.solve()
>>>
>>> dgp_problem.unpack(gp2dcp.retrieve(dcp_problem.solution))
>>> print(dgp_problem.value)
>>> print(dgp_problem.variables())

accepts(problem)[source]

A problem is accepted if it is DGP.

apply(problem)[source]

Converts a DGP problem to a DCP problem.

canonicalize_expr(expr, args)[source]

Canonicalize an expression, w.r.t. canonicalized arguments.

invert(solution, inverse_data)[source]

Returns a solution to the original problem given the inverse_data.

Parameters
• solution (Solution) – A solution to a problem that generated the inverse_data.

• inverse_data – The data encoding the original problem.

Returns

A solution to the original problem.

Return type

Solution

## EvalParams¶

class cvxpy.reductions.eval_params.EvalParams(problem=None)[source]

Replaces symbolic parameters with their constant values.

accepts(problem) → bool[source]

States whether the reduction accepts a problem.

Parameters

problem (Problem) – The problem to check.

Returns

True if the reduction can be applied, False otherwise.

Return type

bool

apply(problem)[source]

Replace parameters with constant values.

Parameters

problem (Problem) – The problem whose parameters should be evaluated.

Returns

A new problem where the parameters have been converted to constants.

Return type

Problem

Raises

ParameterError – If the problem has unspecified parameters (i.e., a parameter whose value is None).

invert(solution, inverse_data)[source]

Returns a solution to the original problem given the inverse_data.

## FlipObjective¶

class cvxpy.reductions.flip_objective.FlipObjective(problem=None)[source]

Flip a minimization objective to a maximization and vice versa.

accepts(problem) → bool[source]

States whether the reduction accepts a problem.

Parameters

problem (Problem) – The problem to check.

Returns

True if the reduction can be applied, False otherwise.

Return type

bool

apply(problem)[source]

$$\max(f(x)) = -\min(-f(x))$$

Parameters

problem (Problem) – The problem whose objective is to be flipped.

Returns

• Problem – A problem with a flipped objective.

• list – The inverse data.

invert(solution, inverse_data)[source]

Map the solution of the flipped problem to that of the original.

Parameters
• solution (Solution) – A solution object.

• inverse_data (list) – The inverse data returned by an invocation to apply.

Returns

A solution to the original problem.

Return type

Solution