### Articles

Mathematical Optimization

Optimization algorithms for business, engineering, data analysis and machine learning.

Mathematical optimization is a powerful tool in many real-life application areas. Proceeding from a formal mathematical model simulating the behavior of a practical system, optimization algorithms are applied to minimize a so-called cost function subject to some constraints.

Due to our expertise in numerical optimization and in object-oriented programming, we easily specify, design, and test robust, reliable and effective optimization engines. Their modular architecture makes maintenance and evolution simple. We provide you with the components that fit best to your situation.

We solve problems of maximizing/minimizing a measurable objective given a set of constraints. The solution to an optimization problem often provides insights in weighing the trade-off between the objective and the constraints.

### WE PERFORM IN FOLLOWING AREAS:

• 01Linear Programming
is used in a variety of practical fields to maximize the useful output of a process for a given input. It is used for resource optimization, as long as the constraints and the objective function are linear or can be linearized.

Applications fields: financial management, personnel management, marketing, distribution center allocation, farm planning, inventory control, telecommunication network design, transport model.
• 02Nonlinear Programming
is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
Problems are in general more difficult to solve than linear programming problems, and often the solution found is only a local optimum.

Applications fields: data networks, production planning, energy, engineering, location, lot sizing, miscellaneous, routing, telecommunications, transportation, resource allocation.
• 03Mixed Integer Nonlinear Programming
The mathematical modeling of systems often requires the use of both nonlinear and discrete components.
Discrete decision variables model dichotomies, discontinuities, and general logical relationships. Problems involving both discrete variables and nonlinear constraint functions and are among the most challenging computational optimization problems faced by researchers and practitioners.

Applications fields: management of electricity transmission, contingency analysis and blackout prevention of electric power systems, design of water distribution networks, operational reloading of nuclear reactors, minimization of the environmental impact of utility plants, Investment Portfolio Selection.

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