To plot the objective function value, you can specify using optimoptions(). For example
opts = optimoptions('fmincon', 'PlotFcn', 'optimplotfval');
fmincon(@(x) sum(x.^2.*exp(x)), rand(4,1), [], [], [], [], [], [], [], opts)
You can find the list of available plot functions here: https://www.mathworks.com/help/releases/R2020a/optim/ug/fmincon.html#busog7r-options and you can also create your custom plot function.
To save the value, you will need to use outputFcn, as demonstrated in John's answer here: https://www.mathworks.com/matlabcentral/answers/510713-is-it-possible-to-store-the-intermediate-values-of-fmincon#answer_420002. You can use his FEX package (mentioned in his answer) to avoid the global variable.
