Package index • CVXR

Core classes

Variables, parameters, constants, problems, and constraints

Variable(): Create an Optimization Variable
Parameter(): Create a Parameter
Constant(): Create a Constant Expression
Problem(): Create an Optimization Problem
Minimize(): Create a Minimization Objective
Maximize(): Create a Maximization Objective
Equality(): Create an Equality Constraint
Inequality(): Create an Inequality Constraint
NonNeg(): Create a Non-Negative Constraint
NonPos(): Create a Non-Positive Constraint
Zero(): Create a Zero Constraint
PSD(): Create a Positive Semidefinite Constraint
ExpCone(): Create an Exponential Cone Constraint
SOC(): Create a Second-Order Cone Constraint
PowCone3D(): Create a 3D Power Cone Constraint
PowConeND(): Create an N-Dimensional Power Cone Constraint
FiniteSet(): FiniteSet Constraint

Solve interface

Solving problems and extracting results

psolve(): Solve a Convex Optimization Problem
value(): Get the Numeric Value of an Expression
`value<-`(): Set the Value of a Leaf Expression
dual_value(): Get the Dual Value of a Constraint
status(): Get the Solution Status of a Problem
solution(): Get the Raw Solution Object
problem_data(): Get Problem Data for a Solver
solve_via_data(): Solve via Raw Data
problem_unpack_results(): Unpack Solver Results into a Problem
unpack_results() deprecated: Unpack Results (backward-compatible alias)
solver_stats(): Get Solver Statistics
solver_opts(): Create Solver Options
solver_default_param(): Standard Solver Parameter Mappings
installed_solvers(): List installed solvers
available_solvers() exclude_solvers() include_solvers() set_excluded_solvers(): List available solvers
residual(): Get the Residual of a Constraint
violation(): Get the Violation of a Constraint

Solvers

Solver name constants

SCS_SOLVER OSQP_SOLVER CLARABEL_SOLVER HIGHS_SOLVER MOSEK_SOLVER GUROBI_SOLVER GLPK_SOLVER GLPK_MI_SOLVER ECOS_SOLVER ECOS_BB_SOLVER CPLEX_SOLVER CVXOPT_SOLVER PIQP_SOLVER SCIP_SOLVER XPRESS_SOLVER: Solver Name Constants

Status constants

Solution status values

OPTIMAL INFEASIBLE UNBOUNDED SOLVER_ERROR OPTIMAL_INACCURATE INFEASIBLE_INACCURATE UNBOUNDED_INACCURATE USER_LIMIT INFEASIBLE_OR_UNBOUNDED: Solution Status Constants

Math and standard function dispatch

Standard R functions that work directly on CVXR expressions. abs, exp, log, sqrt, sum, max, min (group generics); norm, mean, diff (S4 generics); sd, var, outer (masking wrappers).

norm() sd() var() outer() diag(): Standard R Functions for CVXR Expressions

Elementwise atoms

Functions applied element-by-element

entr(): Create an entropy atom -x * log(x)
huber(): Create a Huber loss atom
inv_pos(): Inverse position: \(x^{-1}\) (for x > 0)
kl_div(): KL Divergence: x*log(x/y) - x + y
log1p_atom() log1p_expr(): Log(1 + x) – elementwise
logistic(): Logistic function: log(1 + exp(x)) – elementwise
loggamma(): Elementwise log of the gamma function
log_normcdf(): Elementwise log of the standard normal CDF
neg(): Negative part: -min(x, 0)
pos(): Positive part: max(x, 0)
power(): Create a Power atom
scalene(): Scalene penalty: alpha * pos(x) + beta * neg(x)
square(): Square of an expression: x^2
xexp(): x * exp(x) – elementwise

Aggregation atoms

Functions that reduce or summarize entries

sum_entries(): Sum the entries of an expression
max_entries(): Maximum entry of an expression
min_entries(): Minimum entry of an expression
max_elemwise(): Elementwise maximum of expressions
min_elemwise(): Elementwise minimum of expressions
cumsum_axis(): Cumulative sum along an axis
cummax_expr(): Cumulative maximum along an axis
prod_entries(): Product of entries along an axis
log_sum_exp(): Log-sum-exp: log(sum(exp(x)))
sum_squares(): Sum of squares (= quad_over_lin(x, 1))
sum_largest(): Sum of k largest entries
sum_smallest(): Sum of k smallest entries
geo_mean(): (Weighted) geometric mean of a vector
harmonic_mean(): Harmonic mean: n / sum(1/x_i)
ptp(): Peak-to-peak (range): max(x) - min(x)
cvxr_mean(): Mean of an expression
cvxr_std() std(): Standard deviation of an expression
cvxr_var(): Variance of an expression
cvar(): Conditional Value at Risk (CVaR)

Norm and distance atoms

Norm functions and related atoms

cvxr_norm(): Compute a norm of an expression
p_norm(): General p-norm of an expression
norm1(): L1 norm of an expression
norm2() deprecated: Euclidean norm (deprecated alias)
norm_inf(): L-infinity norm of an expression
norm_nuc(): Nuclear norm (sum of singular values)
mixed_norm(): Mixed norm (\(L_{p,q}\) norm): column-wise p-norm, then q-norm
quad_form(): Quadratic form x^T P x
quad_over_lin(): Sum of squares divided by a scalar
matrix_frac(): Matrix fractional function

Linear algebra atoms

Matrix operations and structural atoms

bmat(): Construct a Block Matrix
conv(): 1D discrete convolution
DiagMat(): Extract Diagonal from a Matrix
DiagVec(): Vector to Diagonal Matrix
hstack(): Horizontal concatenation of expressions
vstack(): Vertical concatenation of expressions
kron(): Kronecker product of two expressions
lambda_max(): Maximum eigenvalue
lambda_min(): Minimum eigenvalue
lambda_sum_largest(): Sum of largest k eigenvalues
lambda_sum_smallest(): Sum of smallest k eigenvalues
log_det(): Log-determinant
matrix_trace(): Trace of a square matrix expression
partial_trace(): Partial trace of a tensor product expression
partial_transpose(): Partial transpose of a tensor product expression
reshape_expr(): Reshape an expression to a new shape
sigma_max(): Maximum singular value
upper_tri(): Extract strict upper triangle of a square matrix
vec(): Vectorize an expression (column vector)
vec_to_upper_tri(): Reshape a vector into an upper triangular matrix

Arithmetic and product atoms

Multiplication, dot products, and related

multiply() deprecated: Elementwise multiplication (deprecated)
vdot(): Vector dot product (inner product)
scalar_product(): Scalar product (alias for vdot)
cvxr_outer(): Outer product of two vectors
dotsort(): Weighted sorted dot product
inv_prod(): Reciprocal of product of entries
tr_inv(): Trace of matrix inverse
total_variation(): Total variation of a vector or matrix
tv() deprecated: Total variation (deprecated alias)
cvxr_diff(): Compute kth Order Differences of an Expression

Special atoms

Perspective, DGP, DQCP, and other specialized atoms

perspective(): Perspective Transform
diff_pos(): The difference x - y with domain x > y > 0
resolvent(): Resolvent inverse(sI - X)
one_minus_pos(): The difference 1 - x with domain (0, 1)
eye_minus_inv(): Unity resolvent (I - X) inverse for positive square matrix X
pf_eigenvalue(): Perron-Frobenius eigenvalue of a positive matrix
gmatmul(): Geometric matrix multiplication A diamond X
ceil_expr(): Elementwise Ceiling
floor_expr(): Elementwise Floor
condition_number(): Condition number of a PSD matrix
gen_lambda_max(): Maximum generalized eigenvalue
dist_ratio(): Distance ratio
indicator(): Indicator function for constraints

Logic atoms

Boolean logic operations for mixed-integer problems

And(): Logical AND
Or(): Logical OR
Not(): Logical NOT
Xor(): Logical XOR
implies(): Logical Implication
iff(): Logical Biconditional

Constraint operators

Operators for creating constraints

`%>>%`: Positive Semidefinite Constraint Operator
`%<<%`: Negative Semidefinite Constraint Operator

Expression properties

Query properties of CVXR expressions

curvature(): Get Expression Curvature
expr_sign(): Get the DCP Sign of an Expression
is_affine(): Check if an Expression is Affine
is_concave(): Check if an Expression is Concave
is_constant(): Check if an Expression is Constant
is_convex(): Check if an Expression is Convex
is_dcp(): Check if an Expression is DCP-Compliant
is_dgp(): Check if a Constraint is DGP-Compliant
is_dpp(): Check DPP Compliance
is_dqcp(): Check if Expression is DQCP-Compliant
is_log_log_affine(): Check if Expression is Log-Log Affine
is_log_log_concave(): Check if Expression is Log-Log Concave
is_log_log_convex(): Check if Expression is Log-Log Convex
is_lp(): Check if a Problem is a Linear Program
is_matrix(): Is the Expression a Matrix?
is_mixed_integer(): Check if a Problem is Mixed-Integer
is_nonneg(): Check if Expression is Non-Negative
is_nonpos(): Check if Expression is Non-Positive
is_nsd(): Check if Expression is Negative Semidefinite
is_psd(): Check if Expression is Positive Semidefinite
is_pwl(): Check if Expression is Piecewise Linear
is_qp(): Check if a Problem is a Quadratic Program
is_quadratic(): Check if an Expression is Quadratic
is_quasiconcave(): Check if Expression is Quasiconcave
is_quasiconvex(): Check if Expression is Quasiconvex
is_quasilinear(): Check if Expression is Quasilinear
is_scalar(): Is the Expression a Scalar?
is_symmetric(): Check if Expression is Symmetric
is_vector(): Is the Expression a Vector?
is_zero(): Check if Expression is Zero
length_expr(): Length of a Vector (Last Nonzero Index)
size(): Get Expression Size
name(): Get Expression Name
id(): Get Expression ID
set_label(): Set a Label on a Constraint

Problem properties

Extract components from a Problem object

objective(): Get Problem Objective (read-only)
constraints(): Get Problem Constraints (read-only)
variables(): Get the Variables in an Expression
parameters(): Get the Parameters in an Expression
constants(): Get the Constants in an Expression

Utilities

Helpers and introspection

as_cvxr_expr(): Convert a value to a CVXR Expression
visualize(): Visualize the Canonicalization Pipeline of a CVXR Problem
to_latex(): Convert CVXR Object to LaTeX
expr_H(): Conjugate-Transpose of an Expression
make_sparse_diagonal_matrix(): Make a CSC sparse diagonal matrix
rel_entr(): Relative Entropy: x*log(x/y)

Data

Example datasets

cdiac: Global Monthly and Annual Temperature Anomalies (degrees C), 1850-2015 (Relative to the 1961-1990 Mean) (May 2016)
dspop: Direct Standardization: Population
dssamp: Direct Standardization: Sample

Deprecated

Backward-compatible aliases (use the new names instead)

get_problem_data() deprecated: Get Problem Data for a Solver (deprecated)
problem_status() deprecated: Get the Solution Status of a Problem (deprecated)
problem_solution() deprecated: Get the Raw Solution Object (deprecated)