Optimal Choice of a Penalty Function: Simplest Case of Algorithm Design
In the previous lessons, we learned how continuous mathematics is useful in choosing and debugging the existing algorithms and programs. With this lesson, we will start learning how continuous mathematics can be useful in designing new algorithms. We will consider the simplest case of design problems, in which both the constraints and the objective are well defined and described by differentiable functions. For such problem, we describe the penalty function method, and then formulate and solve the problem of choosing the best penalty function.
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