linkedin / dualip

DuaLip: Dual Decomposition based Linear Program Solver

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DuaLip: Dual Decomposition based Linear Program Solver

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DuaLip is an extreme-scale Linear Program (LP) solver based on Apache Spark. It solves structured LP problems of the following form arising from web-applications:

minimize        c'x
subject to      Ax <= b
                x_i in C_i  for i in 1,2,...,I

where x = (x_1, ..., x_I) is the full vector of optimization variables, x_i is the vector of optimization variables associated with one i, and A,b,c and C_i are user-supplied data.

It is a distributed solver that solves a perturbation of the LP problem at scale via gradient-based algorithms on the smooth dual of the perturbed LP with computational guarantees. Dualip can easily scale to problems in trillions of variables.

This library was created by Yao Pan, Kinjal Basu, Rohan Ramanath, Konstantin Salomatin, Amol Ghoting, Sathiya Keerthi and Miao Cheng from LinkedIn.


Copyright 2021 LinkedIn Corporation All Rights Reserved.

Licensed under the BSD 2-Clause License (the "License"). See License in the project root for license information.


Extreme Scale

DuaLip is specifically developed to tackle problems arising in web applications that usually have hundreds of millions of users and millions of items, pushing the number of optimization variables into the trillions range (if not more). It uses a dual decomposition technique to be able to scale to such large problems. For details and a wide range of applications, see Ramanath et. al. (2021) and Basu et. al. (2020).


Although we follow first-order gradient methods to solve the problem, we implement several highly efficient algorithms for each of the component steps. This allows us to scale up 20x over a naive implementation. Please see Ramanath et. al. (2021) for a comparative study.

Modular Design

In our implementation, any problem can be formulated through a highly modular approach.

Each of these components is highly flexible and can be easily customized to add new solvers, or new types of projections for different constraints sets C_i. New formulations can also be added by appropriately stitching together these different components.

Detects Infeasibility

We have incorporated simple checks on infeasibility (see Appendix D of our paper). This helps the end user to appropriately tweak their problem space.

Extensive Logging

We have added extensive logging to help users understand whether the solver has converged to a good approximate solution.

Warm start

We allow the user to input an initial estimate of the dual solution, if she is familiar with the problem space. This allows for very efficient solving of the overall problem.

For more details of these features please see the full wiki.


Building the Library

It is recommended to use Scala 2.11.8 and Spark 2.3.0. To build, run the following:

./gradlew build

This will produce a JAR file in the ./dualip/build/libs/ directory.

If you want to use the library with Spark 2.4, you can specify this when running the build command.

./gradlew build -PsparkVersion=2.4.3

Tests typically run with the test task. If you want to force-run all tests, you can use:

./gradlew cleanTest test --no-build-cache

Using the JAR File

Depending on the mode of usage, the built JAR can be deployed as part of an offline data pipeline, depended upon to build jobs using its APIs, or added to the classpath of a Spark Jupyter notebook or a Spark Shell instance. For example:

$SPARK_HOME/bin/spark-shell --jars target/dualip_2.11.jar

Usage Examples

For detailed example usage, please see the Getting Started wiki.


If you would like to contribute to this project, please review the instructions here.


Implementations of some methods in DuaLip were inspired by other open-source libraries. Discussions with several LinkedIn employees influenced aspects of this library. A full list of acknowledgements can be found here.


DuaLip has been created on the basis of the following research paper. If you cite DuaLip, please use the following:

  author       = {Ramanath, Rohan, and Keerthi, Sathiya S. and Basu, Kinjal and Salomatin, Konstantin and Yao, Pan},
  title        = {Efficient Algorithms for Global Inference in Internet Marketplaces},
  journal      = {arXiv preprint arXiv:2103.05277},
  year         = {2021},
  url          = {}

  title        = {{ECLIPSE}: An Extreme-Scale Linear Program Solver for Web-Applications},
  author       = {Basu, Kinjal and Ghoting, Amol and Mazumder, Rahul and Pan, Yao},
  booktitle    = {Proceedings of the 37th International Conference on Machine Learning},
  pages        = {704--714},
  year         = {2020},
  volume       = {119},
  series       = {Proceedings of Machine Learning Research},
  month        = {13--18 Jul},
  publisher    = {PMLR},
  pdf          = {},
  url          = {}

    author     = {Ramanath, Rohan, and Keerthi, Sathiya S. and Basu, Kinjal and Salomatin, Konstantin and Yao, Pan and Ghoting, Amol},
    title      = {{DuaLip}: Dual Decomposition based Linear Program Solver, version 1.0.0},
    url        = {},
    month      = mar,
    year       = 2021