MATLAB: Matlab optimization module problem

fminconglobalMATLABminimumoptimizationoptimoptions

I am using matlab R2016a. I am using optimization module for my application

trying to find the minimum in my function (below is the main optimization

lines). There are two variables that I'm interested to optimize them to

make the function minimum. The objective function has lots of local

minimums. Unfortunately each run gave me different variables. Sometimes

there's 30% or more difference between runs results. And sometimes the

optimization module get stuck in one of the local minimums. I tried to tune

every tolerance and step size but no success so far and I don't get a

consistent final results for my two variables. Could you please help me how

can I tune the Options to have a quicker and consistent result. ; options =

optimoptions('fmincon','Display','iter','Algorithm','

sqp','MaxFunctionEvaluations',1500,'MaxIterations',1500,'

ConstraintTolerance',1.0e-10,'OptimalityTolerance',1.0e-10,'StepTolerance',1.0e-10);;

estparam=fmincon(@objfun,estparam0,A,b,Aeq,beq,lb,ub,[],options)

Best Answer

If you have access to the Global Optimization Toolbox, you may use “GlobalSearch” or “MultiStart” features of the toolbox to obtain the global minimum to your problem.

https://www.mathworks.com/help/releases/R2016b/gads/globalsearch-class.html

https://www.mathworks.com/help/releases/R2016b/gads/multistart-class.html

In addition, another potential workaround is to use the function “patternsearch”

Example:

>> options = optimoptions('patternsearch','Display','iter','MaxFunctionEvaluations',1500,'MaxIterations',1500,'ConstraintTolerance',1.0e-10,'StepTolerance',1.0e-10);

>> estparam=patternsearch(@objfun,estparam0,A,b,Aeq,beq,lb,ub,[],options)

https://www.mathworks.com/help/releases/R2016b/gads/patternsearch.html

Finally, you may also try calling “fmincon” multiple times in a “for” or “parfor” loop, giving different initial guesses each time and keeping track of the best solution. This will not necessarily guarantee a global minimum, but it will likely yield a better and more consistent answer.

Related Solutions

MATLAB: Does the “ga” function violate a linear constraint even though the exitflag was 1

Although the "exitflag" is 1, this does not necessarily mean that all of the constraints are satisfied. The "ga" function uses the "ConstraintTolerance" setting to determine the "exitflag" of 1. For more detail on this, please refer to the documentation page for "ga" at the following link:https://www.mathworks.com/help/gads/ga.html#outputarg_fvalI recommend tightening the "ConstrantTolerance" setting to see if it fixes the violation. You can do this using the "optimoptions" function. Please see the following example:

options = optimoptions('ga','ConstraintTolerance',1.0000e-06)

For more information on what options you can set, please refer to this documentation link:

https://www.mathworks.com/help/optim/ug/optim.problemdef.optimizationproblem.optimoptions.html

MATLAB: Displaying names of multiple variables in a plot

Let us assume that you have following variables created in your workspace:

>> v1 = rand(10,1);

>> v2 = rand(10,1)+1;

>> v3 = rand(10,1)+2;

>> v4 = rand(10,1)+3;

>> v5 = rand(10,1)+4;

>> v6 = rand(10,1)+5;

>> v7 = rand(10,1)+6;

>> v8 = rand(10,1)+7;

>> v9 = rand(10,1)+8;

1. You can concatenate all the variables into a matrix and then you can plot them as you iterate over matrix of variables using "for" loop with "hold on" command. To accomplish that you can execute following code:

>> variables = [v1,v2,v3,v4,v5,v6,v7,v8,v9]; % This creates (10-by-9) matrix containing variables as individual columns. All the variables should have same number of values else MATLAB will throw an error.

>> for i = 1:9

>> plot(dates, variables(:,i)); % Variables are plotted column by column.

>> hold on;

>> end

>> varNames = {'y = IEI','y = IEF','y = SHY','y = TLH','y = TLT','y = TIP','y = AGZ','y = CIU','y = HYG'}; % Create a cell array of strings for legend

>> legend(varNames, 'Location', 'SouthWest'); % Provide the cell array as an argument to "legend" function. Number of entries in cell array should be same as number of variables.

>> xlabel('Date');

>> ylabel('Normalized Price');

>> title('Normalized Asset Prices and Benchmark');

>> datetick('x');

>> grid on;

>> hold off;

2. You can concatenate all the variables into a matrix and provide that matrix as input to the plot function which will plot the data for you. You do not have to use "hold on" command in this approach. To accomplish this you can execute:

>> plot(dates,variables); % Variables are plotted column by column.