A new version of CVX 2.0 beta has been posted to the web site. Please go get it. We’ve fixed a handful of bugs, but most importantly, we’ve completed the licensing engine. As with the previous beta, this version comes with a license for CVX Professional that expires on November 30, 2012—a little over three weeks away. After that date, you’ll need a license to use the CVX Professional features.

If you are an academic user, you can obtain a license key at no charge. Just visit our Academic license request page and fill out the online form. An active university email address is required, as well as the username and host ID of the computer you are using. If everything checks out, you should receive your license key within minutes. Please note that these license keys require this latest beta release to operate (build 883 or later).

Commercial users will need to purchase a CVX Professional license from us to continue using Gurobi and MOSEK with CVX after the conclusion of the beta period. Feel free to send us an email at sales@cvxr.com for a quote.

Lastly, let us take this opportunity to promote the CVX Forum! This is a community-driven Q&A site where you can find answers to a variety of common usage questions posed by users of CVX. If you have a question that hasn’t yet been asked, of course, you can ask it. And if you have an answer that others may find useful, you can provide it, too. We truly hope that over time the CVX Forum will become a rich database of expertise in disciplined convex programming, CVX, and TFOCS.

We’re hard at work getting ready for the full release of CVX 2.0. We have incorporated some great feedback from our users already, including bug fixes submitted to our help desk and issues raised on our Q&A site.

We are committed to offering academic licenses at no charge—and with as little inconvenience as possible. I have been hard at work building the infrastructure to support that. But it looks like that work will not be finished by the time the beta period ends in two weeks—on October 31, 2012. For that reason, I have created a new beta license key that extends the beta period another month—to November 30, 2012.

To grab the new license key, click on this link to be taken to our help desk site. There you will find a link to download the new license key, as well as instructions for installing it.

Remember, a license key is required only if you need to use CVX with commercial solvers. If you are content with SDPT3 or SeDuMi, a license is unnecessary.

EDIT: We’ve posted a new version of CVX 2.0 beta on the download page that includes the license key, as well as a couple of minor fixes.

Gurobi and MOSEK, the first commercial solvers we have connected to CVX, support mixed-integer models: models with one or more variables constrained to assume integer or even binary (0/1) values. Such variables can be used not just in linear programs, but nonlinear convex programs as well.

We have decided to introduce the ability to specify integer and binary variables into CVX models as well. To use this feature, simply add the integer or binary keyword to the relevant variable declaration; for example:

variable x(10) integer;
variable y(3,3) binary;

Models with integer and binary variables must still obey all of the same disciplined convex programming rules that CVX enforces for continuous models. For this reason, we are calling these models mixed-integer disciplined convex programs, or MIDCPs.

Danger! Danger!

Mixed-integer DCPs are not convex.

As with mixed-integer linear and quadratic programs (MILPs/MIQPs), MIDCPs are theoretically intractable. In practice, your results will vary. Solving them requires the combination of a continuous optimization algorithm, such as an interior-point method, and an exhaustive search, such as a branch-and-bound. In some cases, your model will be solved globally after only a few branches. In other cases, the solver will fail to find a global solution in any reasonable amount of time.

Furthermore, solvers for MIDCPs are less mature than those devoted specifically to MILPs/MIQPs. Most of the developments that have improved the performance of MILP solvers map logically to MIDCPs, but MIDCPs present new challenges. We hypothesize that solver performance will be more sensitive to problem size with MIDCPs than with MILPs, and that the best results will come with models that make only sparing use of integer variables.

Non-convex constraints as MIDCP constraints

One of the more interesting consequences of MIDCP support is that, in limited cases, a nonconvex model can be transformed in to an MIDCP. For instance, suppose x is a vector variable, and l and u are constant vectors. If you were to specify the constraint

l <= abs(x) <= u;

in CVX, you would get the dreaded Disciplined convex programming error: message. But in fact, this constraint can be represented as an MIDCP by introducing a vector of binary variables:

varaible xb(size(x)) binary;
l - xb .* ( l + u ) <= x <= u - xb .* ( l + u );

For a nonlinear example, consider these constraints:

max(norm(x),norm(y)) <= 2;
min(norm(x),norm(y)) <= 1;

The first constraint is convex, the second is not. But together they can be specified in an MIDCP:

binary variable nb;
norm(x) <= 1 + nb;
norm(y) <= 2 - nb;

We emphasize that the ability to convert nonconvex constraints to MIDCP form is the exception rather than the rule. For instance, the constraint

1 <= norm(x) <= 2;

looks very similar to our first example, but it cannot be converted to an MIDCP. Furthermore, CVX will not perform these conversions for you; you will have to identify and perform them yourself. Do not ignore convexity during the modeling process, assuming that you will be able to convert your model to an MIDCP after the fact!

Solver support

Neither of CVX’s free solvers supports MIDCPs. Gurobi and MOSEK are currently the only choices for these problem types. Academic users will be able to use either solver (or both!) at no charge. Commercial users can use them by purchasing a CVX Professional License.

We hope to add support for a free mixed-integer solver in a future version of CVX. We are currently studying the use of GLPK, the GNU Linear Programming Kit. Of course, as the name implies, GLPK will only support models that can be converted to LPs or MILPs. If a reliable, free solver that supports both integer variables and conic constraints becomes available, we will certainly consider it; please contact us!

Can a mixed-integer problem truly be disciplined?

Among those of you who know us well, there might be some surprise at our decision to include mixed-integer support. After all, we have been, and remain, very strong advocates for a deliberate approach to convex programming. Indeed, we coined the term disciplined convex programming to describe our philosophy: that the best way to exploit convexity is not to search for it after the model is constructed, but rather to make convexity an explicit goal of the modeling process itself.

We hold that a proper use of MIDCPs still requires a disciplined approach to model building. As we said above, non-convex models representable as MIDCPs will be the exception, not the rule; it is still necessary to build models with convexity as a goal, not an artifact. The performance limits of MIDCP solvers will tend to limit the use of integer and binary variables in CVX models.

There is no doubt that the addition of MIDCPs to CVX is an experiment for us. It will also be an experiment for our users and our solver partners as well. We look forward to seeing the new applications that arise when modelers can add modest numbers of integer constraints to their models. And we look forward to seeing the algorithms for mixed-integer convex programming improve as a suite of “difficult” test problems accumulates.

We are proud to announce the release of CVX 2.0. We have added some interesting new features, big and small, and are looking forward to seeing our users exploit them!

Some of the highlights include:

• Solve problems using commercial solvers Gurobi and MOSEK
• Support for binary and integer variables
• A new support infrastructure
• The ability to save preferences, like your preferred solver, precision settings, and so forth, between MATLAB sessions, using the cvx_save_prefs command
• A revamped cvx_setup installation script
• Support dropped for Matlab 7.4 and earlier

Using Gurobi and MOSEK

MOSEK ApS and Gurobi Optimization are two great companies that provide high-performance, well-supported solvers for convex programming. Both companies have been fantastic about supporting our efforts to connect CVX to their solvers; you’ll hear more our about our work together in the coming weeks. We believe that they will make great choices for use with the models our users wish to solve.

The addition of support for commercial solvers is part of our commercialization strategy for CVX Research. CVX will remain free of charge for all users when paired with the free solvers SDPT3 and SeDuMi; and commercial solver support will be free for all academic users as well. But starting with the final version of CVX 2.0, commercial customers will need to purchase a CVX Professional License to use CVX with Gurobi or MOSEK.

We will share more about product and pricing details over the course of this beta period. But for now, version 2.0 beta includes a built-in, time-limited CVX Professional License. Thus all users, both academic and commercial, are free to use CVX with Gurobi and MOSEK for the duration of the beta period. Simply make sure that Matlab sees mosekopt and/or gurobi in its path before you run cvx_setup.

Mixed integer support

It is now possible to specify that one or more of your variables must assume integer or binary (0/1) values. We call such models mixed integer disciplined convex programs, or MIDCPs. We’ve created an separate post devoted to some of the very real caveats and cautions that come with adding integer support; click here to see it.

A new support infrastructure

CVX has reached a download pace of over 10,000 downloads per year? The acceptance of our software into the research community has truly been amazing—and challenging. Supporting all of our users via email, as we have done for the last 6 years, entirely at our expense, is simply no longer tenable. So we’re creating a new support infrastructure so that we believe will truly help the CVX user community. Please see here for more details.

Support for (very) old versions of Matlab dropped

Version 1.22 of CVX required Matlab version 6.5 or later. Starting with 2.0, we have dropped support for versions 7.4 and older, and now support Matlab only on versions 7.5 or later. We did this to help streamline our development process and to enable us to take advantage of some of the more modern features of the MATLAB language.

Of course, Matlab 7.5 is over five years old now, and we are certain that nearly all of our users are using even newer versions. Nevertheless, if for some reason you absolutely must run CVX on Matlab 7.4 or earlier, you can still download CVX 1.22 from our web site.