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CVXR

Disciplined Convex Optimization

An object-oriented modeling language for disciplined convex programming (DCP) as described in Fu, Narasimhan, and Boyd (2020, <doi:10.18637/jss.v094.i14>). It allows the user to formulate convex optimization problems in a natural way following mathematical convention and DCP rules. The system analyzes the problem, verifies its convexity, converts it into a canonical form, and hands it off to an appropriate solver to obtain the solution. Interfaces to solvers on CRAN and elsewhere are provided, both commercial and open source.

Functions (403)

Abs-class

The Abs class.

AddExpression-class

The AddExpression class.

AffAtom-class

The AffAtom class.

Atom-class

The Atom class.

AxisAtom-class

The AxisAtom class.

BinaryOperator-class

The BinaryOperator class.

CBC_CONIC-class

An interface to the CBC solver

CPLEX_CONIC-class

An interface for the CPLEX solver

CPLEX_QP-class

An interface for the CPLEX solver.

CVXOPT-class

An interface for the CVXOPT solver.

CVXR-package

CVXR: Disciplined Convex Optimization in R

CallbackParam-class

The CallbackParam class.

Canonical-class

The Canonical class.

Canonicalization-class

The Canonicalization class.

Chain-class

The Chain class.

Complex2Real-class

Lifts complex numbers to a real representation.

Complex2Real.abs_canon

Complex canonicalizer for the absolute value atom

Complex2Real.add

Helper function to sum arguments.

Complex2Real.at_least_2D

Upcast 0D and 1D to 2D.

Complex2Real.binary_canon

Complex canonicalizer for the binary atom

Complex2Real.canonicalize_expr

Canonicalizes a Complex Expression

Complex2Real.canonicalize_tree

Recursively Canonicalizes a Complex Expression.

Complex2Real.conj_canon

Complex canonicalizer for the conjugate atom

Complex2Real.constant_canon

Complex canonicalizer for the constant atom

Complex2Real.hermitian_canon

Complex canonicalizer for the hermitian atom

Complex2Real.imag_canon

Complex canonicalizer for the imaginary atom

Complex2Real.join

Helper function to combine arguments.

Complex2Real.lambda_sum_largest_canon

Complex canonicalizer for the largest sum atom

Complex2Real.matrix_frac_canon

Complex canonicalizer for the matrix fraction atom

Complex2Real.nonpos_canon

Complex canonicalizer for the non-positive atom

Complex2Real.norm_nuc_canon

Complex canonicalizer for the nuclear norm atom

Complex2Real.param_canon

Complex canonicalizer for the parameter matrix atom

Complex2Real.pnorm_canon

Complex canonicalizer for the p norm atom

Complex2Real.psd_canon

Complex canonicalizer for the positive semidefinite atom

Complex2Real.quad_canon

Complex canonicalizer for the quadratic atom

Complex2Real.quad_over_lin_canon

Complex canonicalizer for the quadratic over linear term atom

Complex2Real.real_canon

Complex canonicalizer for the real atom

Complex2Real.separable_canon

Complex canonicalizer for the separable atom

Complex2Real.soc_canon

Complex canonicalizer for the SOC atom

Complex2Real.variable_canon

Complex canonicalizer for the variable atom

Complex2Real.zero_canon

Complex canonicalizer for the zero atom

ConeDims-class

Summary of cone dimensions present in constraints.

ConeMatrixStuffing-class

Construct Matrices for Linear Cone Problems

ConicSolver-class

The ConicSolver class.

ConicSolver.get_coeff_offset

Return the coefficient and offset in Ax + b.

ConicSolver.get_spacing_matrix

Returns a sparse matrix that spaces out an expression.

Conjugate-class

The Conjugate class.

Constant-class

The Constant class.

ConstantSolver-class

The ConstantSolver class.

Constraint-class

The Constraint class.

Conv-class

The Conv class.

CumMax-class

The CumMax class.

CumSum-class

The CumSum class.

CvxAttr2Constr-class

The CvxAttr2Constr class.

Dcp2Cone-class

Reduce DCP Problem to Conic Form

Dcp2Cone.entr_canon

Dcp2Cone canonicalizer for the entropy atom

Dcp2Cone.exp_canon

Dcp2Cone canonicalizer for the exponential atom

Dcp2Cone.geo_mean_canon

Dcp2Cone canonicalizer for the geometric mean atom

Dcp2Cone.huber_canon

Dcp2Cone canonicalizer for the huber atom

Dcp2Cone.indicator_canon

Dcp2Cone canonicalizer for the indicator atom

Dcp2Cone.kl_div_canon

Dcp2Cone canonicalizer for the KL Divergence atom

Dcp2Cone.lambda_max_canon

Dcp2Cone canonicalizer for the lambda maximization atom

Dcp2Cone.lambda_sum_largest_canon

Dcp2Cone canonicalizer for the largest lambda sum atom

Dcp2Cone.log1p_canon

Dcp2Cone canonicalizer for the log 1p atom

Dcp2Cone.log_canon

Dcp2Cone canonicalizer for the log atom

Dcp2Cone.log_det_canon

Dcp2Cone canonicalizer for the log determinant atom

Dcp2Cone.log_sum_exp_canon

Dcp2Cone canonicalizer for the log sum of the exp atom

Dcp2Cone.logistic_canon

Dcp2Cone canonicalizer for the logistic function atom

Dcp2Cone.matrix_frac_canon

Dcp2Cone canonicalizer for the matrix fraction atom

Dcp2Cone.normNuc_canon

Dcp2Cone canonicalizer for the nuclear norm atom

Dcp2Cone.pnorm_canon

Dcp2Cone canonicalizer for the p norm atom

Dcp2Cone.power_canon

Dcp2Cone canonicalizer for the power atom

Dcp2Cone.quad_form_canon

Dcp2Cone canonicalizer for the quadratic form atom

Dcp2Cone.quad_over_lin_canon

Dcp2Cone canonicalizer for the quadratic over linear term atom

Dcp2Cone.sigma_max_canon

Dcp2Cone canonicalizer for the sigma max atom

Dgp2Dcp-class

Reduce DGP problems to DCP problems.

Dgp2Dcp.add_canon

Dgp2Dcp canonicalizer for the addition atom

Dgp2Dcp.constant_canon

Dgp2Dcp canonicalizer for the constant atom

Dgp2Dcp.div_canon

Dgp2Dcp canonicalizer for the division atom

Dgp2Dcp.exp_canon

Dgp2Dcp canonicalizer for the exp atom

Dgp2Dcp.eye_minus_inv_canon

Dgp2Dcp canonicalizer for the (I - X)^-1 atom

Dgp2Dcp.geo_mean_canon

Dgp2Dcp canonicalizer for the geometric mean atom

Dgp2Dcp.log_canon

Dgp2Dcp canonicalizer for the log atom

Dgp2Dcp.mul_canon

Dgp2Dcp canonicalizer for the multiplication atom

Dgp2Dcp.mulexpression_canon

Dgp2Dcp canonicalizer for the multiplication expression atom

Dgp2Dcp.nonpos_constr_canon

Dgp2Dcp canonicalizer for the non-positive constraint atom

Dgp2Dcp.norm1_canon

Dgp2Dcp canonicalizer for the 1 norm atom

Dgp2Dcp.norm_inf_canon

Dgp2Dcp canonicalizer for the infinite norm atom

Dgp2Dcp.one_minus_pos_canon

Dgp2Dcp canonicalizer for the 1-x atom

Dgp2Dcp.parameter_canon

Dgp2Dcp canonicalizer for the parameter atom

Dgp2Dcp.pf_eigenvalue_canon

Dgp2Dcp canonicalizer for the spectral radius atom

Dgp2Dcp.pnorm_canon

Dgp2Dcp canonicalizer for the p norm atom

Dgp2Dcp.power_canon

Dgp2Dcp canonicalizer for the power atom

Dgp2Dcp.prod_canon

Dgp2Dcp canonicalizer for the product atom

Dgp2Dcp.quad_form_canon

Dgp2Dcp canonicalizer for the quadratic form atom

Dgp2Dcp.quad_over_lin_canon

Dgp2Dcp canonicalizer for the quadratic over linear term atom

Dgp2Dcp.sum_canon

Dgp2Dcp canonicalizer for the sum atom

Dgp2Dcp.trace_canon

Dgp2Dcp canonicalizer for the trace atom

Dgp2Dcp.zero_constr_canon

Dgp2Dcp canonicalizer for the zero constraint atom

DgpCanonMethods-class

DGP canonical methods class.

Diag-int

Turns an expression into a DiagVec object

DiagMat-class

The DiagMat class.

DiagVec-class

The DiagVec class.

Diff-int

Takes the k-th order differences

DiffPos

The DiffPos atom.

DivExpression-class

The DivExpression class.

ECOS-class

An interface for the ECOS solver

ECOS.dims_to_solver_dict

Utility method for formatting a ConeDims instance into a dictionary that can be supplied to ECOS.

ECOS_BB-class

An interface for the ECOS BB solver.

Elementwise-class

The Elementwise class.

EliminatePwl-class

The EliminatePwl class.

EliminatePwl.abs_canon

EliminatePwl canonicalizer for the absolute atom

EliminatePwl.cummax_canon

EliminatePwl canonicalizer for the cumulative max atom

EliminatePwl.cumsum_canon

EliminatePwl canonicalizer for the cumulative sum atom

EliminatePwl.max_elemwise_canon

EliminatePwl canonicalizer for the elementwise maximum atom

EliminatePwl.max_entries_canon

EliminatePwl canonicalizer for the max entries atom

EliminatePwl.min_elemwise_canon

EliminatePwl canonicalizer for the elementwise minimum atom

EliminatePwl.min_entries_canon

EliminatePwl canonicalizer for the minimum entries atom

EliminatePwl.norm1_canon

EliminatePwl canonicalizer for the 1 norm atom

EliminatePwl.norm_inf_canon

EliminatePwl canonicalizer for the infinite norm atom

EliminatePwl.sum_largest_canon

EliminatePwl canonicalizer for the largest sum atom

Entr-class

The Entr class.

EqConstraint-class

The EqConstraint class

EvalParams-class

The EvalParams class.

Exp-class

The Exp class.

ExpCone-class

The ExpCone class.

Expression-class

The Expression class.

EyeMinusInv-class

The EyeMinusInv class.

FlipObjective-class

The FlipObjective class.

GLPK-class

An interface for the GLPK solver.

GLPK_MI-class

An interface for the GLPK MI solver.

GUROBI_CONIC-class

An interface for the GUROBI conic solver.

GUROBI_QP-class

An interface for the GUROBI_QP solver.

GeoMean-class

The GeoMean class.

HStack-class

The HStack class.

HarmonicMean

The HarmonicMean atom.

Huber-class

The Huber class.

Imag-class

The Imag class.

Index-class

The Index class.

IneqConstraint-class

The IneqConstraint class

InverseData-class

The InverseData class.

KLDiv-class

The KLDiv class.

Kron-class

The Kron class.

LambdaMax-class

The LambdaMax class.

LambdaMin

The LambdaMin atom.

LambdaSumLargest-class

The LambdaSumLargest class.

LambdaSumSmallest

The LambdaSumSmallest atom.

Leaf-class

The Leaf class.

ListORConstr-class

A Class Union of List and Constraint

Log-class

The Log class.

Log1p-class

The Log1p class.

LogDet-class

The LogDet class.

LogSumExp-class

The LogSumExp class.

Logistic-class

The Logistic class.

MOSEK-class

An interface for the MOSEK solver.

MOSEK.parse_dual_vars

Parses MOSEK dual variables into corresponding CVXR constraints and dual values

MOSEK.recover_dual_variables

Recovers MOSEK solutions dual variables

MatrixFrac-class

The MatrixFrac class.

MatrixStuffing-class

The MatrixStuffing class.

MaxElemwise-class

The MaxElemwise class.

MaxEntries-class

The MaxEntries class.

Maximize-class

The Maximize class.

MinElemwise-class

The MinElemwise class.

MinEntries-class

The MinEntries class.

Minimize-class

The Minimize class.

MixedNorm

The MixedNorm atom.

MulExpression-class

The MulExpression class.

Multiply-class

The Multiply class.

Neg-int

An alias for -MinElemwise(x, 0)

NegExpression-class

The NegExpression class.

NonPosConstraint-class

The NonPosConstraint class

NonlinearConstraint-class

The NonlinearConstraint class.

Norm-atom

The Norm atom.

Norm1-class

The Norm1 class.

Norm2-atom

The Norm2 atom.

NormInf-class

The NormInf class.

NormNuc-class

The NormNuc class.

OSQP-class

An interface for the OSQP solver.

Objective-arith

Arithmetic Operations on Objectives

Objective-class

The Objective class.

OneMinusPos-class

The OneMinusPos class.

PSDConstraint-class

The PSDConstraint class.

PSDWrap-class

The PSDWrap class.

Parameter-class

The Parameter class.

PfEigenvalue-class

The PfEigenvalue class.

Pnorm-class

The Pnorm class.

Pos-int

An alias for MaxElemwise(x, 0)

Power-class

The Power class.

Problem-arith

Arithmetic Operations on Problems

Problem-class

The Problem class.

ProdEntries-class

The ProdEntries class.

Promote-class

The Promote class.

Qp2SymbolicQp-class

The Qp2SymbolicQp class.

QpMatrixStuffing-class

The QpMatrixStuffing class.

QpSolver-class

A QP solver interface.

QuadForm-class

The QuadForm class.

QuadOverLin-class

The QuadOverLin class.

Rdict-class

The Rdict class.

Rdictdefault-class

The Rdictdefault class.

Real-class

The Real class.

Reduction-class

The Reduction class.

ReductionSolver-class

The ReductionSolver class.

Reshape-class

The Reshape class.

SCS-class

An interface for the SCS solver

SCS.dims_to_solver_dict

Utility method for formatting a ConeDims instance into a dictionary that can be supplied to SCS.

SCS.extract_dual_value

Extracts the dual value for constraint starting at offset.

SOC-class

The SOC class.

SOCAxis-class

The SOCAxis class.

SigmaMax-class

The SigmaMax class.

SizeMetrics-class

The SizeMetrics class.

Solution-class

The Solution class.

SolverStats-class

The SolverStats class.

SolvingChain-class

The SolvingChain class.

SpecialIndex-class

The SpecialIndex class.

SumEntries-class

The SumEntries class.

SumLargest-class

The SumLargest class.

SumSmallest

The SumSmallest atom.

SumSquares

The SumSquares atom.

SymbolicQuadForm-class

The SymbolicQuadForm class.

TotalVariation

The TotalVariation atom.

Trace-class

The Trace class.

Transpose-class

The Transpose class.

UnaryOperator-class

The UnaryOperator class.

UpperTri-class

The UpperTri class.

VStack-class

The VStack class.

Variable-class

The Variable class.

Wrap-class

The Wrap class.

ZeroConstraint-class

The ZeroConstraint class

abs

Absolute Value

accepts

Reduction Acceptance

are_args_affine

Are the arguments affine?

bmat

Block Matrix

canonicalize

Canonicalize

cdiac

Global Monthly and Annual Temperature Anomalies (degrees C), 1850-2015 (Relative to the 1961-1990 Mean) (May 2016)

complex-atoms

Complex Numbers

complex-methods

Complex Properties

cone-methods

Second-Order Cone Methods

constr_value

Is Constraint Violated?

construct_intermediate_chain-Problem-list-method

Builds a chain that rewrites a problem into an intermediate representation suitable for numeric reductions.

construct_solving_chain

Build a reduction chain from a problem to an installed solver.

conv

Discrete Convolution

cummax_axis

Cumulative Maximum

cumsum_axis

Cumulative Sum

curvature

Curvature of Expression

curvature-atom

Curvature of an Atom

curvature-comp

Curvature of Composition

curvature-methods

Curvature Properties

cvxr_norm

Matrix Norm (Alternative)

diag

Matrix Diagonal

diff

Lagged and Iterated Differences

dim_from_args

Atom Dimensions

domain

Domain

dot-LinOpVector__new

Create a new LinOpVector object.

dot-LinOpVector__push_back

Perform a push back operation on the args field of LinOp

dot-LinOp__args_push_back

Perform a push back operation on the args field of LinOp

dot-LinOp__get_dense_data

Get the field dense_data for the LinOp object

dot-LinOp__get_id

Get the id field of the LinOp Object

dot-LinOp__get_size

Get the field size for the LinOp object

dot-LinOp__get_slice

Get the slice field of the LinOp Object

dot-LinOp__get_sparse

Get the sparse flag field for the LinOp object

dot-LinOp__get_sparse_data

Get the field named sparse_data from the LinOp object

dot-LinOp__get_type

Get the field named type for the LinOp object

dot-LinOp__new

Create a new LinOp object.

dot-LinOp__set_dense_data

Set the field dense_data of the LinOp object

dot-LinOp__set_size

Set the field size of the LinOp object

dot-LinOp__set_slice

Set the slice field of the LinOp Object

dot-LinOp__set_sparse

Set the flag sparse of the LinOp object

dot-LinOp__set_sparse_data

Set the field named sparse_data of the LinOp object

dot-LinOp__set_type

Set the field named type for the LinOp object

dot-LinOp__size_push_back

Perform a push back operation on the size field of LinOp

dot-LinOp__slice_push_back

Perform a push back operation on the slice field of LinOp

dot-LinOp_at_index

Return the LinOp element at index i (0-based)

dot-ProblemData__get_I

Get the I field of the ProblemData Object

dot-ProblemData__get_J

Get the J field of the ProblemData Object

dot-ProblemData__get_V

Get the V field of the ProblemData Object

dot-ProblemData__get_const_to_row

Get the const_to_row field of the ProblemData Object

dot-ProblemData__get_const_vec

Get the const_vec field from the ProblemData Object

dot-ProblemData__get_id_to_col

Get the id_to_col field of the ProblemData Object

dot-ProblemData__new

Create a new ProblemData object.

dot-ProblemData__set_I

Set the I field in the ProblemData Object

dot-ProblemData__set_J

Set the J field in the ProblemData Object

dot-ProblemData__set_V

Set the V field in the ProblemData Object

dot-ProblemData__set_const_to_row

Set the const_to_row map of the ProblemData Object

dot-ProblemData__set_const_vec

Set the const_vec field in the ProblemData Object

dot-ProblemData__set_id_to_col

Set the id_to_col field of the ProblemData Object

dot-build_matrix_0

Get the sparse flag field for the LinOp object

dot-build_matrix_1

Get the sparse flag field for the LinOp object

dot-decomp_quad

Compute a Matrix Decomposition.

dot-p_norm

Internal method for calculating the p-norm

dspop

Direct Standardization: Population

dssamp

Direct Standardization: Sample

dual_value-methods

Get and Set Dual Value

entr

Entropy Function

exp

Natural Exponential

expression-parts

Parts of an Expression Leaf

extract_dual_value

Gets a specified value of a dual variable.

extract_mip_idx

Coalesces bool, int indices for variables.

eye_minus_inv

Unity Resolvent

format_constr

Format Constraints

geo_mean

Geometric Mean

get_data

Get Expression Data

get_dual_values

Gets the values of the dual variables.

get_id

Get ID

get_np

Get numpy handle

get_problem_data

Get Problem Data

get_sp

Get scipy handle

grad

Sub/Super-Gradient

graph_implementation

Graph Implementation

group_constraints

Organize the constraints into a dictionary keyed by constraint names.

harmonic_mean

Harmonic Mean

hstack

Horizontal Concatenation

huber

Huber Function

Identification Number

import_solver

Import Solver

installed_solvers

List installed solvers

inv_pos

Reciprocal Function

invert

Return Original Solution

is_dcp

DCP Compliance

is_dgp

DGP Compliance

is_mixed_integer

Is Problem Mixed Integer?

is_qp

Is Problem a QP?

is_stuffed_cone_constraint

Is the constraint a stuffed cone constraint?

is_stuffed_cone_objective

Is the objective a stuffed cone objective?

is_stuffed_qp_objective

Is the QP objective stuffed?

kl_div

Kullback-Leibler Divergence

kronecker

Kronecker Product

lambda_max

Maximum Eigenvalue

lambda_min

Minimum Eigenvalue

lambda_sum_largest

Sum of Largest Eigenvalues

lambda_sum_smallest

Sum of Smallest Eigenvalues

leaf-attr

Attributes of an Expression Leaf

linearize

Affine Approximation to an Expression

log

Logarithms

log_det

Log-Determinant

log_log_curvature

Log-Log Curvature of Expression

log_log_curvature-atom

Log-Log Curvature of an Atom

log_log_curvature-methods

Log-Log Curvature Properties

log_sum_exp

Log-Sum-Exponential

logistic

Logistic Function

matrix_frac

Matrix Fraction

matrix_prop-methods

Matrix Properties

matrix_trace

Matrix Trace

max_elemwise

Elementwise Maximum

max_entries

Maximum

mean

Arithmetic Mean

min_elemwise

Elementwise Minimum

min_entries

Minimum

mip_capable

Solver Capabilities

mixed_norm

Mixed Norm

mul_elemwise

Elementwise multiplication operator

multiply

Elementwise Multiplication

name

Variable, Parameter, or Expression Name

neg

Elementwise Negative

norm

Matrix Norm

norm1

1-Norm

norm2

Euclidean Norm

norm_inf

Infinity-Norm

norm_nuc

Nuclear Norm

one_minus_pos

Difference on Restricted Domain

p_norm

P-Norm

perform

Perform Reduction

pf_eigenvalue

Perron-Frobenius Eigenvalue

pos

Elementwise Positive

power

Elementwise Power

problem-parts

Parts of a Problem

prod_entries

Product of Entries

project-methods

Project Value

psd_coeff_offset

Given a problem returns a PSD constrain

psolve

Solve a DCP Problem

quad_form

Quadratic Form

quad_over_lin

Quadratic over Linear

reduce

Reduce a Problem

resetOptions

Reset Options

reshape_expr

Reshape an Expression

residual-methods

Constraint Residual

retrieve

Retrieve Solution

scaled_lower_tri

Utility methods for special handling of semidefinite constraints.

scalene

Scalene Function

setIdCounter

Set ID Counter

sigma_max

Maximum Singular Value

sign

Sign of Expression

sign-methods

Sign Properties

sign_from_args

Atom Sign

size

Size of Expression

size-methods

Size Properties

sqrt

Square Root

square

Square

sum_entries

Sum of Entries

sum_largest

Sum of Largest Values

sum_smallest

Sum of Smallest Values

sum_squares

Sum of Squares

to_numeric

Numeric Value of Atom

transpose

Matrix Transpose

tri_to_full

Expands lower triangular to full matrix.

Total Variation

unpack_results

Parse output from a solver and updates problem state

upper_tri

Upper Triangle of a Matrix

validate_args

Validate Arguments

validate_val

Validate Value

value-methods

Get or Set Value

vec

Vectorization of a Matrix

vectorized_lower_tri_to_mat

Turns symmetric 2D array into a lower triangular matrix

vstack

Vertical Concatenation

CVXR

Disciplined Convex Optimization

v1.0-10

Apache License 2.0 | file LICENSE

Authors

Anqi Fu [aut, cre], Balasubramanian Narasimhan [aut], David W Kang [aut], Steven Diamond [aut], John Miller [aut], Stephen Boyd [ctb], Paul Kunsberg Rosenfield [ctb]

Initial release

CVXR

Functions (403)

CVXR

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