Optimization Concepts and Applications in Engineering
Cambridge University Press, Mar 28, 2011 - Computers - 463 pages
It is vitally important to meet or exceed previous quality and reliability standards while at the same time reducing resource consumption. This textbook addresses this critical imperative integrating theory, modeling, the development of numerical methods, and problem solving, thus preparing the student to apply optimization to real-world problems. This text covers a broad variety of optimization problems using: unconstrained, constrained, gradient, and non-gradient techniques; duality concepts; multiobjective optimization; linear, integer, geometric, and dynamic programming with applications; and finite element-based optimization. In this revised and enhanced second edition of Optimization Concepts and Applications in Engineering, the already robust pedagogy has been enhanced with more detailed explanations, an increased number of solved examples and end-of-chapter problems. The source codes are now available free on multiple platforms. It is ideal for advanced undergraduate or graduate courses and for practicing engineers in all engineering disciplines, as well as in applied mathematics.
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1 Preliminary Concepts
2 OneDimensional Unconstrained Minimization
3 Unconstrained Optimization
4 Linear Programming
5 Constrained Minimization
6 Penalty Functions Duality and Geometric Programming
7 Direct Search Methods for Nonlinear Optimization
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active constraints algorithm basic variable bound branch and bound Chapter coefficients column computer program Consider contour convergence convex function convex set corresponding cost defined derivative descent direction design variables determine direction vector discussed dual Engineering equality constraints equations evaluate Example f(xk feasible directions feasible region Fibonacci Figure finite element function f function value given go to step gradient methods Hessian Hessian matrix implemented inequality constraints initial integer iteration KKT conditions Lagrange multipliers Lagrangian line search linear programming local minimum Matlab matrix maximize maximum minimize f node nonbasic Nonlinear Programming objective function obtain optimization problem optimum parameter penalty function plot point x0 positive definite primal quadratic reduced satisfied shown in Fig simplex method solved starting point steepest descent structure tableau techniques tion truss updated xk+1 zero