A new command named optimize has been added. It realises an optimisation loop in Spice Opus. When we run particular optimisation method on a given circuit with optimize command, a general optimisation loop is performed and it is always the same. Its algorithm is as follows:

do
   if number of iterations > max break
   change parameter values
   verify explicit constraints and correct parameter values if necessary
   execute all analysis commands (analysis 0, analysis 1, ..., analysis N)
   number of iterations = number of iterations + 1
   if not implicit constraint 0 or not implicit constraint 1 or ...
       or not implicit constraint M continue
   calculate the cost function
while termination criteria not satisfied

Number of iterations is checked in every iteration. This way the user has some kind of control over the optimisation algorithm and an infinitive optimisation loop (in case of no convergence) is avoided. The optimisation method, which was chosen, is hidden in the way of changing parameter values. If one parameter violate its explicit constraint, its value is corrected to the explicit border. More analyses lines can be defined with optimize analysis commands. They are performed in order and produce necessary results for verifying implicit constraints and evaluating the cost function. If at least one implicit constraint is violated, than algorithm continues with next iteration. Otherwise the cost function is calculated and terminating criteria decides whether the loop will continue or stop.

The optimize command is placed on top of Nutmeg by its function. In fact it just prepares commands in Nutmeg language and executes them in an appropriate order, what leads to optimising process. But on the other hand optimize command is written as an additional Nutmeg command and can be used as one.

The optimize command also generates special group of data (plot). It is named optimizex, where x repesents a plot number. It contains a vector called parameter with final parameter values, a vector called cost with values of the cost function in each iteration, and vectors with parameter values in each iteration.

When the optimize command finishes and finds some optimal parameter values, which are better than initial values, the initial parameter values are changed to optimal ones. That way we can proceed with the next optimize command (maybe with some other method) on the same circuit from the best known point as initial guess.

If the initial_guess option is set (equal or greater than 1), the above is not true. In this case the initial parameter values are set to the values where parameter space was not searched yet. This way many dimensional parameter spaces can be searched by successive optimisation processes. The value of initial_guess option gives the weight factor of the point with the greatest value of the cost function. The weight factor of the point with the smallest value is always 1.

One can choose among several optimisation methods which are coded in the optimize command:

• steepest descent
• Newton's method
• Davidon-Fletcher-Powell's method
• random search
• grid search method
• search along coordinate axes
• Powell's method
• Hooke-Jeeves's method
• constrained simplex method
• simple genetic algorithm
• simulated annealing algorithm
• parallel simulated annealing with differential evolution
• checking cost function in axes directions through current point
• evaluating cost function across whole parameter space

Further description of a particular method can be found in the literature. Here are brief descriptions of optimisation methods and their parameters which can be manually adjusted.

Steepest Descent (steepest_descent)

If the expression for the i-th component of the gradient of the cost function is not given, then it is calculated numerically. All parameters, that are to be optimised, have to be given before this method is chosen. The parameters of the method are:

Newton's Method (newton)

Gradient and Hesse matrix of the cost function are calculated numerically. The parameters of the method are:

Davidon-Fletcher-Powell's method (davidon_fletcher_powell)

If the expression for the i-th component of the gradient of the cost function is not given, then it is calculated numerically. All parameters, that are to be optimised, have to be given before this method is chosen. The parameters of the method are:

Random Search (monte_carlo)

Parameter distribution is regarded only if direction = no. On the other hand parameters r, epsilon and number_of_iterations are taken into account when direction != no. The parameters of the method are:

Grid Search Method (grid_search)

The parameters of the method are:

Search Along Coordinate Axes (axis_search)

The parameters of the method are:

Powell's Method (powell)

The parameters of the method are:

Hooke-Jeeves's Method (hooke_jeeves)

The parameters of the method are:

Constrained Simplex Method (complex)

The parameters of the method are:

Simple Genetic Algorithm (genetic)

The parameters of the method are:

Simulated Annealing Algorithm (simulated_annealing)

The parameters of the method are:

Parallel Simulated Annealing with Differential Evolution Algorithm (psade)

Several simulated annealing processes in parallel interacting through differential evolution. The parameters of the method are:

Checking cost function in axes directions through current point (cost_profile)

The parameter of the method is:

Evaluating cost function across whole parameter space (parameter_space)

The parameters of the method are:

optimize [command]