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Format: 1 online resource (xvvii, 653 pages) : , illustrations

ISBN: 9781118032930 , 1118032934 , 9781118031186 , 1118031180

Content: A thorough and highly accessible resource for analysts in a broad range of social sciences. Optimization: Foundations and Applications presents a series of approaches to the challenges faced by analysts who must find the best way to accomplish particular objectives, usually with the added complication of constraints on the available choices. Award-winning educator Ronald E. Miller provides detailed coverage of both classical, calculus-based approaches and newer, computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinear models and quickly moves on to dis.

Note: Front Matter -- Foundations: Linear Methods. Foundations: Linear Methods -- Matrix Algebra -- Systems of Linear Equations -- Foundations: Nonlinear Methods. Foundations: Nonlinear Methods -- Unconstrained Maximization and Minimization -- Constrained Maximization and Minimization -- Applications: Iterative Methods for Nonlinear Problems. Applications: Iterative Methods for Nonlinear Problems -- Solving Nonlinear Equations -- Solving Unconstrained Maximization and Minimization Problems -- Applications: Constrained Optimization in Linear Models. Applications: Constrained Optimization in Linear Models -- Linear Programming: Fundamentals -- Linear Programming: Extensions -- Linear Programming: Interior Point Methods -- Applications: Constrained Optimization in Nonlinear Models. Applications: Constrained Optimization in Nonlinear Models -- Nonlinear Programming: Fundamentals -- Nonlinear Programming: Duality and Computational Methods -- Answers to Selected Problems -- Index. , Foundations: Linear Methods , Matrix Algebra , Matrices: Definition and General Representation , Algebra of Matrices , Matrix Operations: Addition and Subtraction , Matrix Definitions: Equality and the Null Matrix , Matrix Operations: Multiplication , Matrix Definitions: The Identity Matrix , Matrix Operations: Transposition , Matrix Operations: Partitioning , Additional Definitions and Operations , Linear Equation Systems: A Preview , Matrix Operations: Division , Geometry of Simple Equation Systems: Solution Possibilities , Geometry of Vectors , Linear Combinations of Vectors , Geometry of Multiplication by a Scalar , Geometry of Addition (and Subtraction) , Additional Vector Geometry , Linear Dependence and Independence , Quadratic Forms , Basic Structure of Quadratic Forms , Rewritten Structure of Quadratic Forms , Principal Minors and Permutation Matrices , Sign of a Quadratic Form , Systems of Linear Equations , 2 [times] 2 Case Again , 3 [times] 3 Case , Numerical Illustrations , Summary of 2 [times] 2 and 3 [times] 3 Solution Possibilities , N [times] n Case , Consistent Systems [[rho](A) = [rho](A)] , Inconsistent Systems [[rho](A) [not equal rho](A)] , More Matrix Algebra: Inverses for Nonsquare Matrices , M〉 n Case , M 〈n Case , Nonsquare Inverses and Systems of Linear Equations , Fewer Equations than Unknowns (m 〈n) , Consistent Systems [[rho](A) = [rho](A)] , Inconsistent Systems [[rho](A) [not equal rho](A)] , Summary: Fewer Equations than Unknowns , More Equations than Unknowns (m〉 n) , Consistent Systems [[rho](A) = [rho](A)] , Inconsistent Systems [[rho](A) [not equal rho](A)] , Summary: More Equations than Unknowns , Numerical Methods for Solving Systems of Linear Equations , Elementary Matrix Operations and Gaussian Methods , Iterative Methods , Factorization of the Matrix A , Numerical Illustration , Foundations: Nonlinear Methods , Unconstrained Maximization and Minimization , Limits and Derivatives for Functions of One Variable , Limits , Derivative (Algebra) , Derivative (Geometry) , Maximum and Minimum Conditions for Functions of One Variable , (First) Derivative--a Question of Slope , Second Derivative--a Question of Shape , Maxima and Minima Using First and Second Derivatives , Differential , Maxima and Minima with Differentials , Taylor's Series, Concavity, and Convexity of f(x) , Taylor's Series for f(x) , Concavity and Convexity of f(x) , Local, Global and Unique Maxima and Minima , Additional Kinds of Convexity and Concavity , Numerical Examples , Maxima and Minima for Functions of Two Independent Variables , Partial Derivatives, Gradient Vectors, and Hessian Matrices , Maxima and Minima for f(x[subscript 1], x[subscript 2]) , Total Differential for Functions of Two Variables , Taylor's Series, Concavity, and Convexity of f(X) , Taylor's Series for f(X) , Concavity and Convexity of f(X) , Convex Sets , Numerical Illustrations for the f(x[subscript 1], x[subscript 2]) Case , Quasiconcave and Quasiconvex FunctionsH f(x[subscript 1], x[subscript 2]) , Maxima and Minima for Functions of n Independent Variables , First-Order Conditions , Second-Order Conditions , Quasiconcave and Quasiconvex Functions , Quasiconcavity and Quasiconvexity of f(x) , Quasiconcavity and Quasiconvexity of f(X) , Maclaurin's and Taylor's Series , Maclaurin's Series , Taylor's Series , Taylor's Theorem , Constrained Maximization and Minimization , Quadratic Forms with Side Conditions , Maxima and Minima for Functions of Two Dependent Variables , First-Order Conditions: Differentials , First-Order Conditions: Lagrange Multipliers , Second-Order Conditions , Geometry of the First-Order Conditions , Two Examples with Gradients that Are Null Vectors , A Note on the Form of the Lagrangian Function , Extension to More Dependent Variables , First-Order Conditions , Second-Order Conditions , Extension to More Constraints , First-Order Conditions , Second-Order Conditions , Maxima and Minima with Inequality Constraints , Standard Forms for Inequality-Constrained Problems , More on Inequalities and Convex Sets , One Inequality Constraint , More than One Inequality Constraint , A Systematic Approach: The Kuhn-Tucker Method , Further Complications , Applications: Iterative Methods for Nonlinear Problems , Solving Nonlinear Equations , Solutions to f(x) = 0 , Nonderivative Methods , Derivative Methods , Solutions to F(X) = 0 , Nonderivative Methods , Derivative Methods , Finite-Difference Approximations to Derivatives, Gradients, and Hessian Matrices , Functions of One Variable , Functions of Several Variables , Systems of Equations , Hessian Matrices , Sherman-Morrison-Woodbury Formula , Solving Unconstrained Maximization and Minimization Problems , Minimization of f(x) , Simultaneous Methods , Sequential Methods , Parabolic Interpolation , Combined Techniques , Line Search with Derivatives , Minimization of f(X): Nonderivative Methods , Test Functions , Simplex Methods , Sequential Univariate Search , Conjugate Direction Methods , Results for Additional Test Functions , Minimization of f(X): Derivative Methods , Classical Gradient Methods , Restricted Step Methods , Conjugate Gradient Methods , Quasi-Newton (Variable Metric) Methods , Results for Additional Test Functions , Sherman-Morrison-Woodbury Formula Revisited , Symmetric Rank 1 Changes , An Alternative SMW Expression , Symmetric Rank 2 Changes , Another Alternative SMW Expression , Symmetric Rank n Changes (n〉 2) and the Accompanying SMW Expression , Applications: Constrained Optimization in Linear Models , Linear Programming: Fundamentals , Fundamental Structure, Algebra, and Geometry , Illustrative Example , Minimization Problem: Algebra , Maximization Problem: Geometry , Convex Set Theory Again , Simplex Method , Simplex Criterion , Simplex Arithmetic , Duality , Mathematical Relationships and Interpretation , Dual Values in the Simplex Tables , Optimal Solution to the Dual , Sensitivity Analysis , Changes in the Right-Hand Side of a Constraint , Changes in an Objective Function Coefficient , Linear Programming: Extensions , Multiple Optima and Degeneracy , Primal Multiple Optima , Primal Degenerate Optimum , Artificial Variables , Equations as Constraints , Transportation Problem , Fundamental Structure , Numerical Illustration , Assignment Problem , Fundamental Structure , Numerical Illustration , Integer Programming , Geometry of Integer Programs , Complete Enumeration , Gomory's Cutting-Plane Method , Branch-and-Bound Methods , Hierarchical Optimization and Goal Programming , Hierarchical Optimization: Structure , Hierarchical Optimization: Numerical Illustration , An Alternative Hierarchical Optimization Approach , Numerical Illustration of This Alternative Approach , Goal Programming: Structure , Goal Programming: Numerical Illustration , Linear Programming: Interior Point Methods , Introduction to Interior Point Methods , Affine Scaling Interior Point Methods , Direction of Movement , Step Size , Scaling , Starting and Stopping , Path-Following Interior Point Methods , Additional Variations and Implementation Issues , Regular Simplices; Circles and Ellipses , Alternative Scalings

Additional Edition: Print version: Miller, Ronald E. Optimization. New York : Wiley, 2000 ISBN 0471322423

Language: English

Subjects: Economics , Mathematics

Keywords: Electronic books. ; Electronic books. ; Electronic books.

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118032930

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118032930

URL: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118032930