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2.4 MATHEMATICAL PROGRAMMING SOLUTION

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Problem can be directly solved by using mathematical programming techniques through a nonlinear solver. This approach is considered because current available mathematical programming solvers treat sparsity efficiently and are robust. Moreover, they are computationally efficient and provide highly accurate results. In addition, these solvers allow incorporating easily inequality constraints representing physical limits [9].

For instance, problem can be solved by using solver CONOPT [10] or MINOS [11] under the General Algebraic Modeling System (GAMS) [12], which is a high‐level modeling system for mathematical programming. It consists of a language compiler and a set of integrated high‐performance solvers. GAMS is tailored for complex, large‐scale modeling applications and allows building large maintainable models that can be adapted quickly to new situations. Modeling systems similar to GAMS are AMPL [13] and AIMMS [14].

Advances in Electric Power and Energy

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