On Using MOSEK to Solve The MOSEK solvers Large-Scale Linear and - PowerPoint PPT Presentation

On Using MOSEK to Solve Erling D. Andersen On Using MOSEK to Solve The MOSEK solvers Large-Scale Linear and Conic Optimization Problems Facts Availability Using MOSEK Installation An example: Erling D. Andersen Portfolio optimization Portfolio optimization in Python Fusion MOSEK ApS Portfolio optimization in MATLAB Portfolio INFORMS annual meeting optimization: The optimizer API Minneapolis, October 6-9, 2013 Concluding remarks

On Using MOSEK to Solve The MOSEK solvers Erling D. Andersen Facts Availability The MOSEK solvers Facts Availability Using MOSEK Using MOSEK Installation Installation An example: Portfolio optimization An example: Portfolio optimization Portfolio optimization in Portfolio optimization in Python Fusion Python Fusion Portfolio Portfolio optimization in MATLAB optimization in MATLAB Portfolio Portfolio optimization: The optimizer API optimization: The optimizer API Concluding remarks Concluding remarks

Some facts On Using MOSEK to Solve Erling D. Andersen About MOSEK: The MOSEK • Software package for solving optimization problems. solvers Facts Availability • Version 1 released 1999. Using MOSEK • Version 7 released 2013. Installation An example: Portfolio optimization Portfolio Problem types: optimization in Python Fusion Portfolio • Linear + integer variables. optimization in MATLAB Portfolio • Conic quadratic + integer variables. optimization: The optimizer API • Semidefinite optimization. Concluding remarks • Convex quadratic + integer variables. • General convex.

The system On Using MOSEK to Solve Erling D. Andersen The MOSEK solvers Several interfaces: Facts Availability • Fusion API, Optimizer API and toolbox. Using MOSEK • Supports different languages and tools. Installation An example: Portfolio optimization Portfolio One optimization engine: optimization in Python Fusion Portfolio • Written C. optimization in MATLAB Portfolio • Tuned for the large-scale sparse case. optimization: The optimizer API • Exploit hardware features such as AVX instructions. Concluding remarks

Optimizers for continuous problems On Using MOSEK to Solve Problem type Erling D. Andersen Optimizer Network Linear Conic Convex Network simplex + The MOSEK solvers Primal simplex + + Facts Availability Dual simplex + + Using MOSEK Interior-point + + + + Installation An example: Portfolio optimization Portfolio Simplex optimizers optimization in Python Fusion Portfolio • Large-scale sparse. optimization in MATLAB Portfolio • Many options for pricing etc. optimization: The optimizer API Concluding Interior-point remarks • Large-scale sparse with tuned linear algebra. • Parallelized. • Reliable infeasibility detection and reporting.

Optimizers for mixed-integer problems On Using MOSEK to Solve Erling D. Andersen Mixed integer conic The MOSEK solvers • Solves mixed-integer linear and conic quadratic problems. Facts Availability • Parallelized. Using MOSEK Installation • Run-to-run deterministic. An example: Portfolio optimization • Tuned for conic quadratic problems. Portfolio optimization in Python Fusion • No additional charge. Portfolio optimization in MATLAB Portfolio optimization: Mixed integer optimizer The optimizer API • Solves mixed-integer linear and conic quadratic. Concluding remarks • Tuned for linear problems.

Supported platforms and tools On Using MOSEK to Solve Erling D. Andersen Supported platforms operating systems The MOSEK solvers Windows,MAC OSX, Linux Facts Availability Using MOSEK MOSEK interfaces Installation An example: Portfolio AMPL, C/C++, Java, Python, Matlab, Microsoft .NET, R optimization Portfolio optimization in Python Fusion Portfolio Third party products optimization in MATLAB Portfolio AIMMS, GAMS, Frontline Solver, CVX, Woodstock optimization: The optimizer API Concluding Other interfaces remarks COIN OSI, Raven toolbox, Yalmip ...

On Using MOSEK to Solve The MOSEK solvers Erling D. Andersen Facts Availability The MOSEK solvers Facts Availability Using MOSEK Using MOSEK Installation Installation An example: Portfolio optimization An example: Portfolio optimization Portfolio optimization in Portfolio optimization in Python Fusion Python Fusion Portfolio Portfolio optimization in MATLAB optimization in MATLAB Portfolio Portfolio optimization: The optimizer API optimization: The optimizer API Concluding remarks Concluding remarks

On Using MOSEK to Solve The MOSEK solvers Large-Scale Linear and - PowerPoint PPT Presentation

On Using MOSEK to Solve Erling D. Andersen On Using MOSEK to Solve The MOSEK solvers Large-Scale Linear and Conic Optimization Problems Facts Availability Using MOSEK Installation An example: Erling D. Andersen Portfolio optimization

What is Mosek up to January 15, 2019 Erling D. Andersen www.mosek.com Mosek A software

On recent improvements in MOSEK Erling D. Andersen MOSEK ApS, Fruebjergvej 3, Box 16, 2100

Tour de MOSEK 7: The short version Erling D. Andersen MOSEK ApS, Fruebjergvej 3, Box 16, 2100

MOSEK version 9 (work in progress) July 4, 2018 Erling D. Andersen www.mosek.com Mosek A

An overview of MOSEK Erling D. Andersen MOSEK ApS Fruebjergvej 3, Symbion Science park, Box 16

Extending MOSEK with exponential cones ISMP Bordeaux 2018 joachim.dahl@mosek.com www.mosek.com

Solving conic optimization problems using MOSEK December 16th 2017 e.d.andersen@mosek.com

The R-to-MOSEK Optimization Interface Henrik Alsing Friberg MOSEK ApS, Fruebjergvej 3, Box 16,

Exponential cone in MOSEK ISMP2018, Relative Entropy Optimization, 6 July 2018 Micha l

Power and Exponential cones x y 1 | z | and x ye z/y June 27, 2018 Ulf Worse

On Recent Improvements in the Interior-Point Optimizer in MOSEK ISMP2015 14 July 2015

Mixed-integer conic optimization and MOSEK Dagstuhl seminar on MINLP, February 20th 2018 Sven

Mixed-integer conic optimization and MOSEK Dagstuhl seminar on MINLP, February 20th 2018 Sven

Recent Advances In The New Mosek 8 16-November-2016 Erling D. Andersen www.mosek.com

On the Linear Algebra Employed in the MOSEK Conic Optimizer Monday Jul 13 Erling D. Andersen

Introduction to Mosek Modern Optimization in Energy, 28 June 2018 Micha l Adamaszek

Polynomial optimization using MOSEK and Julia ISMP, Pittsburgh, July 12-17, 2015 Joachim Dahl,

Semidefinite Optimization using MOSEK Joachim Dahl ISMP Berlin, August 23, 2012

Modeling with MOSEK Fusion Ulf Worse INFORMS Minneapolis October 5 2013 http://www.mosek.com

Projection and presolve in MOSEK: exponential and power cones ISMP 2018 Henrik A. Friberg

The Mixed-integer Conic Optimizer in MOSEK 23rd International Symposium on Mathematical

Convex Optimization via Cones and MOSEK 9 CO@Work September 2020, online event Sven Wiese

Building large-scale conic optimization models using MOSEK Fusion Andrea Cassioli Erling D.

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