active constraints linprog example lsqlin example quadprog example active set method fmincon medium-scale algorithm linprog medium-scale algorithm lsqlin medium-scale algorithm quadprog medium-scale algorithm sequential quadratic programming (SQP) attainment factor axis crossing. See zero of a function banana function BFGS formula fmincon medium-scale algorithm fminunc medium-scale algorithm bintprog bisection search bound constraints, large-scale box constraints. See bound constraints centering parameter CG. See conjugate gradients complementarity conditions complex variables lsqcurvefit lsqnonlin conjugate gradients constrained minimization large-scale example with bound constraints and banded preconditioner with equality constraints medium-scale example -constraint method constraints linear fmincon fminimax positive continuous derivative gradient methods convex problem curve-fitting categories functions that apply 21 data-fitting categories functions that apply 21 dense columns, constraint matrix DFP formula direction of negative curvature discontinuities discontinuous problems fminsearch fminunc discrete variables dual problem duality gap equality constraints dense columns medium-scale example equality constraints inconsistent warning, quadprog equality constraints, linear large-scale equation solving categories functions that apply 20 error, Out of memory. feasibility conditions feasible point, finding fgoalattain example fixed variables fixed-step ODE solver fminbnd fmincon large-scale example with bound constraints and banded preconditioner with equality constraints medium-scale example fminimax example fminsearch fminunc large-scale example medium-scale example warning messages fseminf fsolve large-scale Jacobian medium-scale analytic Jacobian medium-scale finite difference Jacobian fsolve medium-scale default function arguments 23 function discontinuities functions grouped by category 20 f(x) = one half ||C times x + d|| squared fzero fzmult gangstr Gauss-Newton method (large-scale) nonlinear least-squares Gauss-Newton method (medium-scale) implementation, nonlinear equations implementation, nonlinear least squares least-squares optimization solving nonlinear equations global minimum goal attainment example fgoalattain goaldemo golden section search gradient checking, analytic gradient examples gradient function gradient methods continuous first derivative quasi-Newton unconstrained optimization Hessian modified message Hessian modified twice message Hessian sparsity structure Hessian update stage of SQP implementation Hessian updating methods inconsistent constraints indefinite problems infeasible message infeasible optimization problems infeasible problems infeasible solution warning linprog quadprog inline objects input arguments 23 integer variables interior-point linear programming introduction to optimization Jacobian analytic finite difference large-scale nonlinear equations Jacobian sparsity pattern Kuhn-Tucker equations Lagrange multipliers large-scale linear programming large-scale functionality coverage large-scale methods demos 21 examples least squares categories functions that apply 21 Levenberg-Marquardt method lsqcurvefit medium-scale default lsqnonlin medium-scale default search direction line search fminunc medium-scale default fsolve medium-scale default lsqcurvefit medium-scale default lsqnonlin medium-scale default unconstrained optimization line search strategy linear constraints fmincon fminimax linear equations solve linear least squares constrained large-scale algorithm large-scale example nonnegative unconstrained linear programming implementation large-scale algorithm large-scale example with dense columns in equalities with equalities and inequalities problem linprog large-scale example with dense columns in equalities with equalities and inequalities LIPSOL lower bounds lsqcurvefit lsqlin large-scale example lsqnonlin convergence large-scale example medium-scale example lsqnonneg maximization medium-scale methods demos 22 Mehrotra's predictor-corrector algorithm merit function minimax examples minimax problem, solving minimization categories functions that apply 20 multiobjective optimization examples fgoalattain NCD. See Nonlinear Control Design negative curvature direction in PCG algorithm in trust-region methods negative definite problems Nelder and Mead Newton direction approximate Newton's method systems of nonlinear equations unconstrained optimization no update message nonconvex problems noninferior solution Nonlinear Control Design (NCD) Blockset nonlinear data-fitting fminsearch fminunc lsqnonlin nonlinear equations Newton's method nonlinear equations (large-scale) example with Jacobian solving nonlinear equations (medium-scale) analytic Jacobian example finite difference Jacobian example Gauss-Newton method solving trust-region dogleg method nonlinear least squares fminsearch fminunc large-scale algorithm large-scale example lsqcurvefit lsqnonlin nonlinear programming normal equations normal equations objective function return values optimality conditions linear programming optimget optimization functions by category 20 getting to a global minimum handling infeasibility helpful hints introduction objective function return values troubleshooting unconstrained optimization parameters structure optimget optimset optimset options parameters descriptions 27 possible values utility functions 21 Out of memory. error output arguments 23 output display output function PCG. See preconditioned conjugate gradients preconditioned conjugate gradients algorithm in large-scale linear programming in trust-region methods preconditioner banded in PCG method predictor-corrector algorithm preprocessing linear programming primal problem primal-dual algorithm primal-dual interior-point projection method quadprog medium-scale algorithm sequential quadratic programming (SQP) quadprog large-scale example quadratic programming fmincon large-scale algorithm large-scale example quadprog quasi-Newton method implementation quasi-Newton methods fminunc medium-scale algorithm unconstrained optimization reflective line search reflective steps definition residual revised simplex algorithm Rosenbrock banana function Rosenbrock's function S sampling interval secular equation semi-infinite constraints Sherman-Morrison formula signal processing example simple bounds simplex search unconstrained optimization Simulink, multiobjective example singleton rows solving nonlinear systems of equations sparsity pattern Jacobian sparsity structure, Hessian SQP method fmincon implementation steepest descent stopping criteria, large-scale linear programming structural rank subspace determination of subspace, two-dimensional systems of nonlinear equations solving trust region trust-region dogleg method (medium-scale) implementation for nonlinear equations systems of nonlinear equations two-dimensional subspace unbounded solutions warning linprog quadprog unconstrained minimization fminsearch fminunc large-scale example medium-scale example one dimensional unconstrained optimization upper bounds variable-step ODE solver warning equality constraints inconsistent, quadprog infeasible solution, linprog infeasible solution, quadprog stuck at minimum, fsolve unbounded solutions, linprog unbounded solutions, quadprog warnings displayed weighted sum strategy zero curvature direction zero finding zero of a function, finding ||C times x minus d|| squared