What Is Optimization Toolbox?

2 TutorialBecause the iterative display was set using optimset, theresultsdisplayedareResiduals: Primal Dual Upper Duality TotalInfeas Infeas Bounds Gap RelA*x-b A'*y+z-w-f {x}+s-ub x'*z+s'*w Error-------------------------------------------------------------Iter 0: 1.67e+003 8.11e+002 1.35e+003 5.30e+006 2.92e+001Iter 1: 1.37e+002 1.33e+002 1.11e+002 1.27e+006 2.48e+000Iter 2: 3.56e+001 2.38e+001 2.89e+001 3.42e+005 1.99e+000Iter 3: 4.86e+000 8.88e+000 3.94e+000 1.40e+005 1.89e+000Iter 4: 4.24e-001 5.89e-001 3.44e-001 1.91e+004 8.41e-001Iter 5: 1.23e-001 2.02e-001 9.97e-002 8.41e+003 5.79e-001Iter 6: 3.98e-002 7.91e-002 3.23e-002 4.05e+003 3.52e-001Iter 7: 7.25e-003 3.83e-002 5.88e-003 1.85e+003 1.85e-001Iter 8: 1.47e-003 1.34e-002 1.19e-003 8.12e+002 8.52e-002Iter 9: 2.52e-004 3.39e-003 2.04e-004 2.78e+002 2.99e-002Iter 10: 3.46e-005 1.08e-003 2.81e-005 1.09e+002 1.18e-002Iter 11: 6.97e-007 3.23e-012 5.64e-007 1.48e+001 1.62e-003Iter 12: 5.10e-007 3.25e-012 3.18e-008 8.32e-001 9.09e-005Iter 13: 5.06e-006 1.43e-010 3.86e-009 7.26e-002 7.94e-006Iter 14: 2.15e-006 2.17e-010 6.53e-012 1.11e-003 1.21e-007Iter 15: 7.34e-008 2.33e-009 3.38e-013 8.62e-008 1.29e-009Optimization terminated.You can see the returned values of exitflag, fval, andoutput:exitflag =1fval =9.1464e+003output =iterations: 15algorithm: 'large-scale: interior point'cgiterations: 208message: 'Optimization terminated.'This time the number of PCG iterations (in output.cgiterations) isnonzerobecause the dense columns in Aeq are detected. Instead of using a sparseCholesky factorization, linprog tries to use the Sherman-Morrison formula tosolve a linear system involving Aeq*Aeq'. If the Sherman-Morrison formula2-76