Changes to CVXPY

This page details changes made to CVXPY over time, in reverse chronological order. CVXPY’s project maintainers currently provide support for CVXPY 1.3 and 1.2, with limited support for 1.1.


CVXPY 1.3 brings many new features, bug fixes, and performance improvements. It introduces a new SciPy-based backend and formalizes the public API of CVXPY as everything that is importable directly from the cvxpy namespace. We plan to introduce a cvxpy.experimental namespace for features in development where the API has not yet been fixed. It is explicitly not a part of our API whether atoms are implemented by functions or classes, e.g. we do not consider replacing cvxpy.power, which is currently a class, with a function to be a breaking change or replacing cp.quad_form which is a function to become a class to be a breaking change. Code of the form cvxpy.power(a, b) is guaranteed to remain working.

Constraints and atoms

Solver interfaces

General system improvements

  • Support for native quadratic forms (x.T @ P @ x)

  • The new OpRelEntrConeQuad constraint class is the first major piece of our effort to improve support for quantum information modeling (GSOC project)

  • Continuous performance benchmarking (GSOC project)


We’re taking a big step toward semantic versioning! Our new versioning policy will be to increment the minor version number (the “x” in “CVXPY 1.x.y”) whenever we introduce new features. The patch number (the “y” in “CVXPY 1.x.y”) will only be incremented for bugfixes. We’ll support multiple minor releases of CVXPY at any given time. API-breaking changes will require incrementing the major version number (i.e., moving to CVXPY 2.x.y).

This versioning policy is very different from what we’ve done in the past. Many new features were added after CVXPY 1.1.0 but before CVXPY 1.2.0. These features accumulated over the course of CVXPY 1.1.1 and 1.1.18. We review those features and the new features in CVXPY 1.2.0 below.

Constraints and atoms

  • 1.2.0: added atoms for partial trace and partial transpose, which are important linear operators in quantum information

  • 1.2.0: updated kron so that either argument in kron(A, B) can be a non-constant affine Expression, provided the other argument is constant. We previously required that A was constant.

  • 1.2.0: added xexp: an atom that implements \(\texttt{xexp}(x) = x e^{x}\).

  • 1.1.14: added loggamma: an atom which approximates the log of the gamma function

  • 1.1.14: added rel_entr: an atom with the same semantics as the SciPy’s “rel_entr”

  • 1.1.8: added log_normcdf: an atom that approximates the log of the Gaussian distribution’s CDF

  • 1.1.8: added power cone constraints

Solver interfaces

  • 1.2.0: support PDLP and GLOP, via OR-Tools

  • 1.1.17: support for SCS 3.0

  • 1.1.14: support for HiGHS (and other LP solvers that come with SciPy)

  • 1.1.12: ECOS, ECOS_BB, and SCS report solver statistics

  • 1.1.12: support warm-start with GUROBI

  • 1.1.8: added a mechanism for users to create solver interfaces without modifying CVXPY source code

  • 1.1.6: rewrote the MOSEK interface; it now dualizes all continuous problems

  • 1.1.4: support for FICO XPRESS

  • 1.1.2: support for SCIP

  • 1.1.2: users can provide their own implementation of a KKT solver for use with CVXOPT

General system improvements

  • 1.1.18: A problem status “infeasible or unbounded”, for use by specific solvers in rare situations

  • 1.1.11: verbose logging

  • 1.1.11: several improvements to CVXPY’s C++ backend rewriting system, “cvxcore.” In particular, CVXPY can now be compiled from source with openmp enabled, which allows canonicalization to take advantage of multithreading.

  • 1.1.6: a “Dualize” reduction



Disciplined parametrized programming or “DPP” is a ruleset for constructing parametrized problems in CVXPY. Taking advantage of DPP can decrease the time it takes CVXPY to repeatedly canonicalize a parametrized problem. DPP also provides the basis for differentiating the map from parameters to the solution of an optimization problem.

CVXPY provides an API where certain solvers can differentiate the map from the parameters of an optimization problem to the optimal solution of that problem. The differentiation abilities are currently only available when SCS is used as the solver. This feature allows for more general sensitivity analysis than is possible when using dual variables alone. It also provides the basis for cvxpylayers. See the tutorial on derivatives and the accompanying papers

Since version 0.4, CVXPY has used * to perform matrix multiplication. As of version 1.1, this behavior is officially deprecated. All matrix multiplication should now be performed with the python standard @ operator. CVXPY will raise a warning if * is used when one of the operands is not a scalar.

New atoms and transforms

CVXPY has long provided abstractions (“atoms” and “transforms”) which make it easier to specify optimization problems in natural ways. The release of CVXPY 1.1 is accompanied by the following new abstractions:

  • A “support function” transform for use in disciplined convex programming.

  • A “scalar product” atom, for appropriate use across all problem classes.

  • A “gmatmul” atom, which captures the DGP equivalent to matrix multiplication.

  • The atoms cp.max and cp.min have been extended for use in DQCP.

  • The python builtin sum is now allowed in DGP.

Breaking changes

We no longer support Python 2 or Python 3.4.

CVXPY 1.1.0 drops the SuperSCS and ECOS_BB solvers.


We added ECOS_BB back in version 1.1.6. Starting with CVXPY 1.2.0, any backwards-incompatible change like removing a solver interface will require incrementing CVXPY’s major version number (e.g., moving from series 1.X to 2.X).


CVXPY 1.1 has substantially improved support for recovering dual variables. Advanced users should be able to recover dual variables to any conic constraint, including exponential-cone and second-order-cone constraints.

This release resolves bugs in detecting when a problem falls into the category of “disciplined quasiconvex programming” (DQCP).

Known issues

DPP problems with many CVXPY Parameters can take a long time to compile.

Disciplined quasiconvex programming (DQCP) doesn’t support DPP.

The XPRESS interface is currently not working. (Fixed in CVXPY 1.1.4.)

Notable patches since CVXPY 1.1.0

Version 1.1.10
  • When NumPy 1.20 was released many users encountered errors in installing or importing CVXPY. Users would see errors like RuntimeError: module compiled against API version 0xe but this version of numpy is 0xd. We changed our build files to avoid this problem, and it should be fixed as of CVXPY 1.1.10. For more information you can refer to this GitHub issue.

Version 1.1.8
  • We have added support for 3-dimensional and N-dimensional power cone constraints. Although, we currently do not have any atoms that take advantage of this constraint. If you want you want to use this type of constraint in your model, you will need to instantiate PowCone3D and/or PowConeND objects manually. Dual variables are not yet implemented for PowConeND objects. At present, only SCS and MOSEK support power cone constraints.

  • We fixed a bug in our MOSEK interface that was introduced in version 1.1.6. The “unknown” status code was not being handled correctly, resulting in ValueErrors rather than SolverErrors. Users can now expect a SolverError when MOSEK returns an “unknown” status code (as was standard before).

Version 1.1.6
  • The ECOS_BB solver (removed in 1.1.0) has been added back as an option. However ECOS_BB will not be called automatically; you must explicitly call prob.solve(solver='ECOS_BB') if you want to use this solver. Refer to our documentation on mixed-integer models for more information.

  • The MOSEK interface has been rewritten and now dualizes all continuous problems. Refer to solver documentation for technical reasons of why we do this, and how to manage MOSEK solver options in the off chance that this change made your solve times increase.


CVXPY 1.0 includes a major rewrite of the CVXPY internals, as well as a number of changes to the user interface. We first give an overview of the changes, before diving into the details. We only cover changes that might be of interest to users.

We have created a script to convert code using CVXPY 0.4.11 into CVXPY 1.0, available here.


  • Disciplined geometric programming (DGP): Starting with version 1.0.11, CVXPY lets you formulate and solve log-log convex programs, which generalize both traditional geometric programs and generalized geometric programs. To get started with DGP, check out the tutorial and consult the accompanying paper.

  • Reductions: CVXPY 1.0 uses a modular system of reductions to convert problems input by the user into the format required by the solver, which makes it easy to support new standard forms, such as quadratic programs, and more advanced user inputs, such as problems with complex variables. See Reductions and the accompanying paper for further details.

  • Attributes: Variables and parameters now support a variety of attributes that describe their symbolic properties, such as nonnegative or symmetric. This unifies the treatment of symbolic properties for variables and parameters and replaces specialized variable classes such as Bool and Semidef.

  • NumPy compatibility: CVXPY’s interface has been changed to resemble NumPy as closely as possible, including support for 0D and 1D arrays.

  • Transforms: The new transform class provides additional ways of manipulating CVXPY objects, byond the atomic functions. While atomic functions operate only on expressions, transforms may also take Problem, Objective, or Constraint objects as input.


A reduction is a transformation from one problem to an equivalent problem. Two problems are equivalent if a solution of one can be converted to a solution of the other with no more than a moderate amount of effort. CVXPY uses reductions to rewrite problems into forms that solvers will accept. The practical benefit of the reduction based framework is that CVXPY 1.0 supports quadratic programs as a target solver standard form in addition to cone programs, with more standard forms on the way. It also makes it easy to add generic problem transformations such as converting problems with complex variables into problems with only real variables.


Attributes describe the symbolic properties of variables and parameters and are specified as arguments to the constructor. For example, Variable(nonneg=True) creates a scalar variable constrained to be nonnegative. Attributes replace the previous syntax of special variable classes like Bool for boolean variables and Semidef for symmetric positive semidefinite variables, as well as specification of the sign for parameters (e.g., Parameter(sign='positive')). Concretely, write

  • Variable(shape, boolean=True) instead of Bool(shape).

  • Variable(shape, integer=True) instead of Int(shape).

  • Variable((n, n), PSD=True) instead of Semidef(n).

  • Variable((n, n), symmetric=True) instead of Symmetric(n).

  • Variable(shape, nonneg=True) instead of NonNegative(shape).

  • Parameter(shape, nonneg=True) instead of Parameter(shape, sign='positive').

  • Parameter(shape, nonpos=True) instead of Parameter(shape, sign='negative').

See Attributes for a complete list of supported attributes. More attributes will be added in the future.

NumPy Compatibility

The following interface changes have been made to make CVXPY more compatible with NumPy syntax:

  • The value field of CVXPY expressions now returns NumPy ndarrays instead of NumPy matrices.

  • The dimensions of CVXPY expressions are given by the shape field, while the size field gives the total number of entries. In CVXPY 0.4.11 and earlier, the size field gave the dimensions and the shape field did not exist.

  • The dimensions of CVXPY expressions are no longer always 2D. 0D and 1D expressions are possible. We will add support for arbitrary ND expressions in the future. The number of dimensions is given by the ndim field.

  • The shape argument of the Variable, Parameter, and reshape constructors must be a tuple. Instead of writing, Parameter(2, 3) to create a parameter of shape (2, 3), you must write Parameter((2, 3)).

  • Indexing and other operations can map 2D expressions down to 1D or 0D expressions. For example, if X has shape (3, 2), then X[:,0] has shape (3,). CVXPY behavior follows NumPy semantics in all cases, with the exception that broadcasting only works when one argument is 0D.

  • Several CVXPY atoms have been renamed:

    • mul_elemwise to multiply

    • max_entries to max

    • sum_entries to sum

    • max_elemwise to maximum

    • min_elemwise to minimum

  • Due to the name changes, we now strongly recommend against importing CVXPY using the syntax from cvxpy import *.

  • The vstack and hstack atoms now take lists as input. For example, write vstack([x, y]) instead of vstack(x, y).


Transforms provide additional ways of manipulating CVXPY objects beyond the atomic functions. For example, the indicator transform converts a list of constraints into an expression representing the convex function that takes value 0 when the constraints hold and \(\infty\) when they are violated. See Transforms for a full list of the new transforms.