Many different mathematical programming techniques can be found in the literature, first order techniques (steepest descent, ...), second order (Newton's method, ...) and so on.
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The methods to solve minimisation problems are direct and indirect
methods. Indirect methods are based on penalty functions (exterior
and interior penalty functions). Direct methods directly manage
the constraints of the problem without modifying the function that
has to be minimised. Many different mathematical programming techniques can be found in the literature, first order techniques (steepest descent, ...), second order (Newton's method, ...) and so on.
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