## Applied Optimization: Formulation and Algorithms for Engineering SystemsThe starting point in the formulation of any numerical problem is to take an intuitive idea about the problem in question and to translate it into precise mathematical language. This book provides step-by-step descriptions of how to formulate numerical problems so that they can be solved by existing software. It examines various types of numerical problems and develops techniques for solving them. A number of engineering case studies are used to illustrate in detail the formulation process. The case studies motivate the development of efficient algorithms that involve, in some cases, transformation of the problem from its initial formulation into a more tractable form. |

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### Contents

Introduction | 1 |

Notation 771 | 13 |

Problems algorithms and solutions | 15 |

Transformation of problems | 103 |

Case studies | 161 |

Algorithms | 186 |

Case studies | 259 |

Algorithms | 285 |

Case studies | 447 |

Algorithms for linear constraints | 463 |

Algorithms for nonlinear constraints | 529 |

Case studies | 559 |

Algorithms for nonnegativity constraints | 607 |

Algorithms for linear constraints | 669 |

Solution of the linearly constrained case studies | 708 |

Algorithms for nonlinear constraints | 723 |

Solution of the case studies | 334 |

Case studies | 363 |

Algorithms | 381 |

Solution of the case studies | 425 |

Solution of the nonlinearly constrained case studies | 748 |

754 | |

762 | |

### Other editions - View all

Applied Optimization: Formulation and Algorithms for Engineering Systems Ross Baldick Limited preview - 2009 |

Applied Optimization: Formulation and Algorithms for Engineering Systems Ross Baldick No preview available - 2009 |

### Common terms and phrases

afﬁne approximation backwards substitution base-case calculate circuit coefﬁcient matrix columns condition number consider constraint function continuous partial derivatives contour sets convergence convex function convex set corresponding deﬁned descent direction diagonal entries differentiable with continuous discussed in Section dual function equality constraints equality-constrained problem evaluated example Exercise f f f feasible set ﬁnd ﬁrst ﬁrst-order necessary conditions formulation function f global ill-conditioned illustrated in Figure inequality constraints initial guess Jacobian Lagrange multipliers linear programming linear simultaneous equations LU factorization MATLAB minimizer of Problem minimum non-linear non-negativity norm null space optimization problem parameters partial derivatives partially differentiable pivot positive deﬁnite power ﬂow quadratic resistor Rn×n rows satisﬁes satisfy Show simultaneous equations solution solve sparse matrix speciﬁed step direction step-size Suppose symmetric Theorem tion transformation transformed problem unconstrained variables vector zero