What Is Optimization Toolbox?

fgoalattainof overattainment is met exactly. Three of the lower bound constraintsarealsoactive.In the preceding design, the optimizer tries to make the objectivesless than the goals. For a worst-case problem where the objectivesmust be as near to the goals as possible, use optimset to set theGoalsExactAchieve option to the number of objectives for which thisis required.Consider the preceding problem when you want all the eigenvaluesto be equal to the goal values. A solution to this problem is found byinvoking fgoalattain with the GoalsExactAchieve option set to 3.options = optimset('GoalsExactAchieve',3);[K,fval,attainfactor] = fgoalattain(...@(K)eigfun(K,A,B,C),K0,goal,weight,[],[],[],[],lb,ub,[],...options)After about seven iterations, a solution isK =-1.5954 1.2040-0.4201 -2.9046fval =-5.0000-3.0000-1.0000attainfactor =1.0859e-20In this case the optimizer has tried to match the objectives to the goals.The attainment factor (of 1.0859e-20) indicates that the goals havebeen matched almost exactly.NotesThis problem has discontinuities when the eigenvalues become complex;this explains why the convergence is slow. Although the underlying8-25