AMPL & Mosek: Precision Unleashed
MOSEK ApS provides optimization software that helps their clients make better decisions. Due to its powerful state-of-the-art simplex solver for linear problems and interior-point conic solver for quadratic and conic problems, MOSEK is widely employed in the technology, financial, energy and forestry industries.
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MOSEK, a high-performance solver developed by MOSEK ApS, a company based in Denmark, is renowned for its efficiency in solving large-scale mathematical optimization problems. It specializes in linear, quadratic, conic, mixed-integer, and convex optimization, catering to a wide array of sectors including finance, energy, telecommunications, and aerospace. Its ability to handle sparse matrix problems and large-scale optimization tasks makes it a preferred choice for both academic research and industrial applications. MOSEK’s robust performance, combined with its seamless integration with modeling languages and systems like AMPL, enables users to solve complex optimization problems with remarkable precision and speed. By offering advanced optimization capabilities, MOSEK empowers professionals and researchers to unlock innovative solutions and make informed, data-driven decisions, making it a pivotal tool in the field of optimization.
Linear, quadratic and conic problems in continuous and integer variables.
Convex quadratic expressions in objectives and constraints; conic quadratic constraints; disjunctive constraints
For continuous problems, primal and dual simplex, interior-point (barrier); for integer problems, advanced branch-and-bound with presolve, feasibility heuristics and cut generators.
Shared-memory parallel processing for barrier, branch-and-bound. Tools to access remote optimization servers. Special facilities for infeasibility diagnosis.
For Python enthusiasts, MOSEK is also accessible as a module with amplpy, blending seamlessly with your Python projects. Explore more about this integration at AMPL Python Integration.# Install Python API for AMPL
$ python -m pip install amplpy
# Install MOSEK
$ python -m amplpy.modules install mosek
Best for individuals running on one machine
$3,000 /year
$650 /year
PTS+PTSON
$1,250 /year
Best for small applications running one process at a time
$4,500 /year
$1,000 /year
PTS+PTSON
$1,900 /year
Best for large teams or applications to run multiple processes simultaneously
$7,000 /year
+$700 /additional CPU
$2,500 /year
+$250 /additional CPU
PTS+PTSON
$4,500 /year
+$450 /additional CPU
Best for individuals running on one machine
$6,000 /purchase
+ $1,200 maintenance annually
$1,300 /year /purchase
+ $260 maintenance annually
$2,500 /purchase
+ $500 maintenance annually
Best for small applications running one process at a time
$9,000 /purchase
+ $1,800 maintenance annually
$2,000 /year /purchase
+ $400 maintenance annually
$3,800 /purchase
+ $760 maintenance annually
Best for large teams or applications to run multiple processes simultaneously
$14,000 /purchase
+ $2,400 maintenance annually
+1,400 /additional CPU
$5,000 /year /purchase
+ $1,000 maintenance annually
+$500 /additional CPU
$9,000 /purchase
+ $1,800 maintenance annually
+$900 /additional CPU
Dynamic License Validation Available (License server)
16 (32 threads)
Contact us for customized licenses tailored for your teams specific needs
Best for individuals running on one machine
$3,000 /yearly subscription
$6,000 /purchase
+ $1,200 maintenance annually
$650 /yearly subscription
$1,300 /purchase
+ $260 maintenance annually
$1,250 /yearly subscription
$2,500 /purchase
+ $500 maintenance annually
Best for small applications running one process at a time
$4,500 /yearly subscription
$9,000 /purchase
+ $1,800 maintenance annually
$1,000 /yearly subscription
$2,000 /purchase
+ $400 maintenance annually
$1,900 /yearly subscription
$3,800 /purchase
+ $760 maintenance annually
Best for large teams or applications to run multiple processes simultaneously
$7,000 /yearly subscription
+ $700 additional CPU
$14,000 /purchase
+ $2,800 maintenance annually + $1,400 additional CPU
$2,500 /yearly subscription
+ $250/additional CPU
$5,000 /purchase
+ $1,000 maintenance annually
+ $500/additional CPU
$4,500 /yearly subscription
+ $450/additional CPU
+ $500/additional CPU
$9,000 /purchase
+ $1,800 maintenance annually
+ $900/additional CPU
MOSEK downloads are available from the My Downloads page of your account at the AMPL Portal, and are included in the bundles that are used for free trials.
The integration of AMPL with the MOSEK solver represents a formidable combination in the realm of optimization, blending AMPL’s intuitive modeling capabilities with MOSEK’s advanced computational efficiency. This synergy is particularly advantageous for solving complex linear, quadratic, conic, and mixed-integer programming problems. AMPL’s user-friendly interface simplifies the model development process, making it accessible to both novices and experienced practitioners. When paired with MOSEK’s robust optimization algorithms, this integration enables swift and accurate solutions for large-scale and computationally intensive models.
In practical applications, the AMPL-MOSEK duo excels in various industries where precision and rapid problem-solving are paramount. For instance, in finance, it facilitates sophisticated portfolio optimization and risk management. In the energy sector, it assists in optimizing network designs and operations. Additionally, in logistics, it enhances vehicle routing and scheduling, leading to significant time and cost savings. The seamless workflow enabled by AMPL’s flexibility in data handling, combined with MOSEK’s prowess in tackling large-scale challenges, allows users to efficiently test different scenarios and make informed decisions. This integration, therefore, stands as a crucial tool for professionals across diverse fields, driving innovative solutions and optimizing operational efficiency with unmatched precision.
MOSEK is a powerhouse optimization solver that transcends mathematical abstractions and delves into the heart of real-world challenges. Its ability to handle complex linear, quadratic, and conic optimization problems makes it a sought-after tool across diverse industries, from finance and healthcare to energy and transportation. Whether you’re navigating the turbulent waters of financial markets, managing the intricate dance of power grids, or optimizing resource allocation in a bustling hospital, MOSEK helps you find optimal solutions, maximize resources, and ultimately achieve your goals.
MOSEK excels at handling linear, mixed-integer linear, quadratic, and conic optimization problems. This includes complex challenges in finance, energy, transportation, scheduling, resource allocation, and design optimization.
MOSEK supports all major 64-bit operating systems (Windows, Linux, macOS) and integrates with various nl-based modeling languages and interfaces. This flexibility allows users to choose their preferred environment for working with MOSEK.
MOSEK is used by leading companies and organizations across various industries. For example, airlines use MOSEK to optimize route planning and aircraft scheduling, reducing fuel consumption and delays. Financial institutions leverage it for portfolio optimization and risk management, maximizing returns while minimizing risk exposure. In the energy sector, MOSEK helps optimize power grid operations and integrate renewable energy sources, contributing to sustainability and grid resilience.
MOSEK uses a combination of interior-point and simplex algorithms along with branch-and-bound methods for different problem types, ensuring efficient and reliable solutions.
MOSEK is designed to handle large and complex optimization problems with millions of variables and constraints. It utilizes advanced memory management and parallelization techniques for scalability.
AMPL’s integration with MOSEK provides advanced data connectivity options, enabling seamless access to databases and APIs for efficient data importation into optimization models and exporting results for analysis or system integration. This feature supports direct interaction with SQL databases via ODBC for real-time data queries, and custom scripts can facilitate API communication, allowing for dynamic data exchange. Such connectivity empowers users to incorporate real-time data into their AMPL models, optimize using MOSEK, and then directly update databases or interact with other services. This integration ensures that optimization processes are deeply embedded within data-driven decision-making frameworks, making the AMPL-MOSEK combo a powerful tool for applications requiring up-to-date data and comprehensive system integration.
MOSEK offers a large set of options to adjust its behaviour. Learn more here.
Mosek website
Mosek for AMPL User’s Guide including option descriptions
Mosek-AMPL interface source code
What’s New in Mosek
