Mathematic Optimization

=0pt 2=HE2 by = 7=8=18 by 1000 7 by8 =.001by 7 1= 1.051 =-2 -12112=-1000pt very basic theory of optimization is introduced here, in order to develop some optimization schemes, useful later for the optimization of real circuits.
The theory of mono-objective optimization involves some properties and theorems regarding finding the minimum of functions, hence the annulling of the functions first derivatives. These results can be extended (with some restrictions) to the case of multivariable functions but when the functions to be optimized are more than one, being optimized simultaneously, the a new theory may be introduced.

The whole goal of this introduction to mathematical optimization is both the developing of reliable algorithms, and the justification of some assumptions made in the chapter 5 (page ), especially for the multi-objective case.

In section 4.1 some mathematical optimization foundations are reported, and in particular in §4.1.1 is shown the theory of mono-objective optimization (unconstrained, §4.1.1.1, and constrained, §4.1.1.2), while in §4.1.2 is shown the theory of multi-objective optimization (unconstrained, §4.1.2.1, and constrained, §4.1.2.2).
The section 4.2 reports the basic and most useful numerical algorithms for optimization purposes: in §4.2.1 some one-dimensional search techniques, in §4.2.2 some multi-dimensional search techniques, and in §4.2.4, §4.2.5 some ``special'' algorithms.
Some conclusion and summarized characteristics are reported in section 4.3.