## Recent Trends in Optimization Theory and ApplicationsWorld Scientific Series in Applicable Analysis (WSSIAA) aims at reporting new developments of high mathematical standard and current interest. Each volume in the series shall be devoted to the mathematical analysis that has been applied or potentially applicable to the solutions of scientific, engineering, and social problems. This volume contains 30 research articles on the theory of optimization and its applications by the leading scientists in the field. It is hoped that the material in the present volume will open new vistas in research.Contributors: B D O Anderson, M Bertaja, O J Boxma, O Burdakov, A Cantoni, D J Clements, B D Craven, J B Cruz, Jr., P Diamond, S V Drakunov, Y G Evtushenko, N M Filatov, I Galligani, J C Geromel, F Giannessi, M J Grimble, G O Guardabassi, D-W Gu, C H Houpis, D G Hull, C Itiki, X Jian, M A Johnson, R E Kalaba, J C Kalkkuhl, M R Katebi, T J Kim, P Kloeden, T Kobylarz, A J Laub, C S Lee, G Leitmann, B-G Liu, J Liu, Z-Q Luo, K A Lurie, P Maponi, J B Matson, A Mess, G Pacelli, M Pachter, I Postlethwaite, T Rapcsak, M C Recchioni, Y Sakawa, S V Savastyuk, K Schittkowski, Y Shi, M A Sikora, D D Siljak, K L Teo, C Tovey, P Tseng, F E Udwadia, H Unbehauen, A Vladimirov, B Vo, J F Whidborne, R Xu, P L Yu, V G Zhadan, F Zirilli. |

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### Contents

On Properties of Newtons Method for Smooth and Nonsmooth | 17 |

Dual Cones in Spaces of Convex Sets and Fuzzy Sets | 35 |

Dual BarrierProjection Methods in Linear Programming | 51 |

Solving Parameter Identification Problems on a ParallelVector | 67 |

Two Algorithms | 107 |

Appells Equations of Motion and the Generalized Inverse Form | 123 |

Plant Optimization and Performance Monitoring | 145 |

Planning for the Big One | 171 |

On Direct Relaxation of Optimal Material Design Problems | 271 |

Upper and Lower Bounds in Quadratic Maximization With Integer | 297 |

Riccati Difference Equations for Discrete Time Spectral Factorization | 311 |

On Global Convergence of an Algorithm for Optimal Control | 327 |

Parameter Estimation in Differential Equations | 353 |

Foundations of Designing Optimal Systems and Contingency Plans | 371 |

A Sliding Mode based LeaderFollower Strategy for MultiLevel | 393 |

A General Approach to Deterministic Annealing | 409 |

Optimal Control Design Using Error Compensation | 193 |

System Identification in Fuzzy Logic Control | 207 |

Control Strategies for an Endemic Disease in the Presence | 221 |

On SecondOrder Sufficient Conditions in Smooth Nonlinear | 239 |

Convergence Analysis of PrimalDual Interior Point | 255 |

Simplified Analysis of an OnLIteration Infeasible | 423 |

Computational Methods for a Class of Optimization | 447 |

Multiobjective Control System A Mixed Optimization Approach | 467 |

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algorithm allocation analysis Appell's equations applied approach approximation assume assumption bounded components computed cone consider constraints contingency plans convergence convex convex cone convex function convex set corresponding cost function decision maker defined denote derivative differential equations discrete dual dynamic estimate exists feasible formulation fuzzy fuzzy logic given global Hence implies inequality input integration invex isolated local minimum iterates Lagrange Lagrange multipliers Lemma linear programming Lyapunov function mapping Math mathematical matrix method minimization Model Ml nonlinear programming objective function obtain operation optimal control optimal solution optimal system optimisation optimization problem ordinary differential equations output parameter performance index polynomial PRCPs primal-dual Proof quadratic programming queues Riccati equation satisfies Scientific Publishing Company second-order sufficient conditions sequence server solving space spectral stationary point statistical process control step techniques Theorem trajectory values variables vector World Scientific Publishing WSSIAA zero Zhang