Before we dive into the SEO tools in the Rich Mom community let me explain to you what will make your SEO efforts go farther than any tool. In this section, we briefly review NMinimize, a built-in general numerical optimization tool. Note that in addition to NMinimize, there are several other optimization-related functions in Mathematica, for example, ConstrainedMin and ConstrainedMax, which will also be discussed shortly. NMinimize[{f, cons}, vars] numerically finds (approximates) the global minimum of an arbitrary linear or nonlinear function f subject to the arbitrary constraints cons. MathOptimizer [38] is a third-party native Mathematica product that enables the global and local solution of the general class of optimization problems encompassed by the CGO model form. MathOptimizer currently consists of two core solver packages and a solver integrator package.
The second solver package implements a convex optimization approach aimed at finding a solution vector that satisfies the Karush-Kuhn-Tucker local optimality conditions. The solver integrator package enables the individual or combined use of these two solver packages; the solvers can also be used separately. The MathOptimizer User Guide [38] is a Mathematica notebook that can be directly invoked through the online Help Browser.
MathOptimizer can be installed and used on all hardware platforms that are suitable to run Mathematica 3.0 or later. Assuming that MathOptimizer is set up using the Mathematica standard directory structure, it can be invoked by the following statement.
We will not go into further, quite extensive, details of the package options and refer the reader to the MathOptimizer User Guide [38] for more information. The output of MathOptimizer consists of the numerically estimated list of optimal solution components, the corresponding objective function value, the lists of the equality and inequality model function values at the solution (including an empty list of equality constraints in this example), the list of the maximal feasibility violation level at the solution, the violation level of the Karush-Kuhn-Tucker equation at the solution, and the violation level of the complementary slackness condition at the solution.
Without going into further details, let us note that the output indicates that the local optimality conditions are satisfied to a fairly high precision and that the solution agrees with the one found by NMinimize to at least precision, in terms of both the optimized arguments and the optimum value. In the next (Contact and Collision Problems) section, we shall illustrate the usage of MathOptimizer and NMinimize in the context of several nontrivial tests that point towards interesting application areas. Table of Contents: What Are Top 10 Website Conversion mistakes, What is Conversion And Why You Should Care?
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We entirely omit the discussion of the underlying theory and algorithms and refer the reader to The Mathematica Book [48], the current documentation [49, 50], and the optimization references listed earlier for details.
The user guide includes installation and technical notes and provides concise mathematical background information and modeling tips. It is available for all Microsoft Windows (95 and later) operating systems, as well as all other platforms that have corresponding current Mathematica implementations. Instead, we shall illustrate the usage of the function Optimize on the last problem discussed in the preceding section. An extensive collection of further numerical examples and illustrative applications formulated in Mathematica is discussed in [29, 39].
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According to the documentation for NMinimize, "The methods are flexible enough to cope with functions that are not differentiable or continuous, and are not easily trapped by local optima. This package is based on an efficient adaptive stochastic search method, combined with a statistical bounding procedure. In addition to a basic usage description, it also discusses a number of simple and more challenging test problems and a few detailed application examples.
Several prominent OS examples are Linux, Macintosh (including Mac OS X), HP-UX, SGI, Solaris, and Sun (Unix flavor) platforms.
Keep in mind, however, that finding a global optimum can be arbitrarily difficult, even without constraints, and so the methods used may fail. The latter provides an estimate of the global optimum value, based on the global sampling results. MathOptimizer software installation and tests with identical file systems were successfully completed using over half a dozen different hardware platforms and operating systems (at the time of this writing, including all the aforementioned platforms).

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