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. |
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 | |
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Applied Optimization: Formulation and Algorithms for Engineering Systems Ross Baldick No preview available - 2009 |
Common terms and phrases
algorithm analysis apply approach approximation assume base-case bound calculate called chapter circuit coefficient columns consider continuous contour sets convergence convex corresponding defined definite Definition described develop diagonal direction discuss dual effort entries equality constraints equations error evaluated example Exercise factorization feasible set Figure find first flow formulation function function f given illustrated inequality constraints involve iteration Jacobian linear lower matrix measurement method minimizer minimum multipliers necessary conditions Newton–Raphson node non-linear norm objective obtain optimization parameters partial derivatives partially differentiable particular pivot positive possible problem production Prove quadratic represent requires respect rows satisfies satisfy Section sensitivity Show shown simultaneous equations solution solve step strictly Suppose Theorem tion transformation typically update variables vector voltage zero