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**ProxSuite** is actively developped and supported by the [Willow](https://www.di.ens.fr/willow/) and [Sierra](https://www.di.ens.fr/sierra/) research groups, joint research teams between [Inria](https://www.inria.fr/en), [École Normale Supérieure de Paris](https://www.ens.fr) and [Centre National de la Recherche Scientifique](https://www.cnrs.fr).
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**ProxSuite** is integrated into the [cvxpy](https://www.cvxpy.org/) modeling language for convex optimization problems.
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## Quick install
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**ProxSuite** is distributed on many well-known package managers.
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Alternative installation procedures are presented in the [Installation Procedure](#installation-procedure) section.
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## ProxSuite main features
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**Proxsuite** is fast:
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- C++ template library,
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- cache friendly.
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**Proxsuite** is versatile, offering through a unified API advanced algorithms specialized for efficiently exploiting problem structures:
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- dense, sparse and matrix free matrix factorization backends,
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- advanced warm-starting options (e.g., equality-constrained initial guess, warm-start or cold-start options from previous results).
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**Proxsuite** is flexible:
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- header only,
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- C++ 17/20 compliant,
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- Python and Julia bindings for easy code prototyping without sacrificing performances.
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**Proxsuite** is extensible.
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**Proxsuite** is reliable and extensively tested, showing the best performances on the hardest problems of the literature.
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**Proxsuite** is supported and tested on Windows, Mac OS X, Unix and Linux.
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## **ProxQP**
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The **ProxQP** algorithm is a numerical optimization approach for solving quadratic programming problems of the form:
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| eps_abs | 1.E-3 | Asbolute stopping criterion of the solver.
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| eps_rel | 0 | Relative stopping criterion of the solver.
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| VERBOSE | False | If set to true, the solver prints information at each loop.
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| default_rho | 1.E-6 | Default rho parameter of result class (i.e., for each initial guess, except WARM_START_WITH_PREVIOUS_RESULT, after a new solve or update, the solver initializes rho to this value).
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| default_mu_eq | 1.E-3 | Default mu_eq parameter of result class (i.e., for each initial guess, except WARM_START_WITH_PREVIOUS_RESULT, after a new solve or update, the solver initializes mu_eq to this value).
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| default_mu_in | 1.E-1 | Default mu_in parameter of result class (i.e., for each initial guess, except WARM_START_WITH_PREVIOUS_RESULT, after a new solve or update, the solver initializes mu_in to this value).
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| compute_timings | True | If set to true, timings will be computed by the solver (setup time, solving time, and run time = setup time + solving time).
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| max_iter | 1.E4 | Maximal number of authorized outer iterations.
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| max_iter_in | 1500 | Maximal number of authorized inner iterations.
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| pri_res | 0 | The primal residual.
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| dua_res | 0 | The dual residual.
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Note finally that when initializing a QP object, by default the proximal step sizes (i.e., rho, mu_eq and mu_in) are set up by the default values defined in the Setting class. Hence, when doing multiple solves, if not specified, their values are re-set respectively to default_rho, default_mu_eq and default_mu_in. A small example is given below in c++ and python.
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