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# Skills & Competence

## Mathematical solver

LEDAS Math Solver is aimed at solving satisfaction/optimization problems under constraints expressed by

• Algebraic equations/inequalities (white-boxes)
• External functions (black-boxes)
• Design tables
• Finite domain constraints
• Geometric and other domain-specific constraints.

To efficiently deal with such problems, LEDAS Math Solver is built as an integration of constraint satisfaction/optimization methods, algorithms of numerical mathematics, efficient system architecture as well as a set of user and programmer tools:

• Methods
• CP. Generalized Constraint Propagation over Interval and Finite Domains
• CPX (CP eXtended). CP-method adjusted for finite-domain problems
• AC4, AC5. Classical methods for achieving Arc-consistency over Finite Domains
• Gauss. Solving systems of linear algebraic equations
• Interior Point. A method of linear programming improved to find sub-optimal solutions
• Newton. Interval variant of Newton method for solving nonlinear equations
• Bisection. General method for locating solutions
• Branch and Bound. Well-known method of solving optimization problems
• Tabular constraint processing (design tables, data bases, etc.)
• Gradient method to deal with so-called black-box satisfaction/optimization widely used in mechanical CAD domain
• Searching sub-optimal solution (with a proof of its sub-optimality)
• Integer Local Search
• A set of global constraint satisfaction methods for finite domains ("alldifferent", "global cardinality" and others)
• Efficient interval library with directed rounding providing verified results
• Transparent C API
• Script
All functionality can be accessed from Python language with the help of PySolver module
• High Level Language
Including: sets, strings, structures; operations with arrays; implicit functions, models

For many benchmarks, LEDAS Solver outperforms all known results of our competitors.

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