| Description |
1 online resource (581 p.) |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Preface -- Author -- 1 Introduction to Lagrange optimization for engineering applications -- 1.1 Significance of this chapter -- 1.2 An optimality formulation based on equality constraints -- 1.2.1 Formulation of Lagrange functions -- 1.2.2 Formulation of gradient vectors -- 1.2.3 Optimality conditions of objective functions constrained by equality functions based on gradient vectors -- finding stationary points based on gradients vectors |
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1.2.4 Optimizations of an objective function constrained by equality functions -- 1.3 An optimality formulation based on inequality constraints -- 1.3.1 KKT (Karush-Kuhn-Tucker Conditions) optimality conditions -- 1.3.2 Formulation of KKT optimality conditions (active and inactive), their implications on economy and structural engineering -- 1.3.3 Optimality examples with inequality conditions -- 1.3.3.1 Example #1 -- Summary -- 1.3.3.2 Example # 2 -- 1.3.3.3 Example # 3 -- 1.4 How many KKT conditions (Kuhn and Tucker, 1951 -- Kuhn and Tucker, 2014) must be considered? -- 1.5 Conclusions |
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2.3.6 ANN-based generalized functions replacing analytical functions -- 2.3.6.1 Formulation of Jacobian and Hessian matrices -- 2.3.6.2 Formulation of Jacobian matrix based on ANN -- 2.3.6.3 Formulation of universally generalizable Hessian matrix based on ANN -- 2.3.6.4 Flow chart for Lagrange-based optimization -- 2.3.6.5 Summary -- 2.4 Examples of optimizing Lagrange functions using ANN-based objective and constraining functions with KKT conditions -- 2.4.1 Purpose of examples -- 2.4.2 Optimization of a fourth-order polynomial with KKT conditions |
| Notes |
Description based upon print version of record |
| Bibliography |
References -- 2 Lagrange optimization using artificial neural network-based generalized functions -- 2.1 Importance of an optimization for engineering designs -- 2.1.1 Significance of ANN-based optimization -- 2.1.2 Why ANN-based generalized functions? -- 2.2 ANN-based Lagrange formulation constrained by inequality functions -- 2.3 ANN-based generalizable objective and constraining functions -- 2.3.1 A limitation of an analytical function-based objective and inequality functions -- 2.3.2 Formulation of ANN-based Lagrange functions and KKT condition |
| Notes |
2.4.2.1 Optimization of a fourth-order polynomial considering inequality constraints based on analytical objective and constraining functions |
| Subject |
Structural optimization.
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Lagrangian functions.
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Lagrangian functions
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Structural optimization
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| Form |
Electronic book
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| ISBN |
9781000804799 |
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1000804798 |
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