## Computational Methods in Optimization Problems |

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### Contents

The Case Where Control Constraints | 92 |

E Examples for Continuous Systems | 96 |

P An Example for a Continuous System | 111 |

### Common terms and phrases

accessory minimum problem adjoint equations adjoint variables algorithm assume boundary conditions boundary value problem calculus of variations canonical systems equations CHAPTER Chemical CM CM CM H conjugate function conjugate gradient method control variable u(t convergence convex function convex set Cross-Current Extraction defined difference equation discrete systems dynamic programming evaluate example problems H CM H UJ Hamiltonian Hessian matrix I&EC Fundamentals inequality constraints Lapidus linear LJ LJ maximum principle maximum transform minimization mole/liter necessary conditions Newton-Raphson method nominal trajectory Nonlinear Programming nth stage numerical objective function obtained Optimal Control optimal solution optimal temperature profile optimization problems partial derivatives Pontryagin's maximum principle reaction reactor system recycle rO rO satisfied second-order gradient method supporting hyperplane terminal conditions terminal constraints Theory tubular reactor UJ H UJ UJ