Optimization Techniques For Solving Complex Problems

Optimization Techniques For Solving Complex Problems-87
This reflects how the ES exponent affects the overall cost for the entire period.

This reflects how the ES exponent affects the overall cost for the entire period.

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In Machine Learning, it is always necessary to continuously evaluate the quality of a data model by using a cost function where a minimum implies a set of possibly optimal parameters with an optimal (lowest) error.

Typically, a utility function or fitness function (maximization), or, in certain fields, an energy function or energy functional.

Here are some examples: Consider the following notation: asks for the maximum value of the objective function 2x, where x may be any real number.

In this case, there is no such maximum as the objective function is unbounded, so the answer is "infinity" or "undefined".

However, the opposite perspective would be valid, too.

Problems formulated using this technique in the fields of physics may refer to the technique as energy minimization, speaking of the value of the function as representing the energy of the system being modeled.

A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution.

In mathematics, conventional optimization problems are usually stated in terms of minimization.

In a convex problem, if there is a local minimum that is interior (not on the edge of the set of feasible elements), it is also the global minimum, but a nonconvex problem may have more than one local minimum not all of which need be global minima.

A large number of algorithms proposed for solving the nonconvex problems – including the majority of commercially available solvers – are not capable of making a distinction between locally optimal solutions and globally optimal solutions, and will treat the former as actual solutions to the original problem.


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