Pseudolinear functions and optimization

Content:
Introduction Convex Sets Convex Functions and Properties Alternative and Separation Theorems Unconstrained and Constrained Optimization Problems Nonlinear Multiobjective Optimization and Pareto Optimality Subdifferential Calculus Optimality Criteria and Duality Pseudolinear Functions: Characterizations and Properties Introduction Differentiable Pseudolinear Functions Local Characterizations of Pseudolinear Functions Second Order Characterizations of Pseudolinear Functions Semilocally Pseudolinear Functions Dini Derivatives and Pseudolinear Functions Characterizations of Locally Lipschitz Pseudolinear Functions using Clarke Subdifferential Weakly Pseudolinear Functions Properties of the Functional Class of Differentiable at a Point Functions Constrained Pseudolinear Optimization Problems: Characterizations of Solution Sets Introduction Characterizations of Solution Sets of Differentiable Pseudolinear Optimization Problems Solution Sets of Linear Fractional Programs Characterizations of Solution Sets of Semilocally Pseudolinear Optimization Problems Characterizations of Solution Sets of Pseudolinear Optimization Problems in Terms of Dini Derivatives Characterizations of Solution Sets of h-Pseudolinear Optimization Problems Characterizations of Solution Sets of Nonsmooth Pseudolinear Optimization Problems Constrained Pseudolinear Optimization Problems: Characterizations of Solutions Sets in Terms of Lagrange Multipliers Introduction Definitions and Preliminaries Pseudolinear Optimization Problems Linear Fractional Programming Problem Vector Linear Fractional Programming Problem Nonsmooth Pseudolinear Optimization Problems with Linear Inequality Constraints Nonsmooth Vector Pseudolinear Optimization Problems with Linear Inequality Constraints Pseudolinearity in terms of Bifunction Necessary Optimality Conditions for a Mathematical Program in terms of Bifunctions Mathematical Program with h-Convex Objective and j h-Pseudolinear Constraints Mathematical Program with h-Pseudolinear Objective and j h-Pseudolinear Constraints Pseudolinear Multiobjective Optimization Introduction Necessary Optimality Conditions Sufficient Optimality Conditions Duality in Multiobjective Programming Multiobjective Fractional Programming Problems Necessary Optimality Conditions Sufficient Optimality Conditions Duality in Multiobjective Fractional Programming Nonsmooth Pseudolinear Multiobjective Optimization Introduction Necessary Optimality Conditions Sufficient Optimality Conditions Duality Theorems Nonsmooth Multiobjective Fractional Programming Necessary Optimality Conditions Sufficient Optimality Conditions Duality Theorems Static Minimax Programming and Pseudolinear Functions Minimax Programming Problems Necessary Optimality Conditions Sufficient Optimality Conditions Duality for Minimax Programming Problem Minimax Fractional Programming Problem Necessary Optimality Conditions Sufficient Optimality Conditions Duality for Minimax Fractional Programming Nonsmooth Static Minimax Programming and Pseudolinear Functions Introduction Definitions and Preliminaries Necessary and Sufficient Optimality Conditions Dual Model I Dual Model II Nonsmooth Multiobjective Pseudolinear Programming: Optimality and Duality in Terms of Bifunctions Introduction Definitions and Preliminaries Necessary and Sufficient Optimality Conditions Duality Theorem Numerical Examples Pseudolinear Multiobjective Semi-Infinite Programming Problems Introduction Necessary and Sufficient Optimality Conditions Duality Theorems Nonsmooth Semi-infinite Programming Problems Necessary and Sufficient Optimality Conditions Duality Theorems Numerical Examples Vector Variational Inequality and Vector Pseudolinear Optimization Problems Introduction Vector Variational Inequality Problems Necessary and Sufficient Optimality Conditions Nonsmooth Vector Variational Inequality Problems Necessary and Sufficient Optimality Conditions Extension of Pseudolinear Functions and Variational Inequality Problems Introduction PPM maps and their Characterizations Affine PPM Maps Characterizations of the Solution Sets of a PPM Variational Inequality Problem Generalizations N Pseudolinear Functions: Characterizations and Properties of Solution Set Introduction Characterizations of Differentiable N-Pseudolinear Functions Characterizations of Solution set of Differentiable N-Pseudolinear Program N-Pseudolinear Functions and Vector Optimization Characterizations of Locally Lipschitz N-Pseudolinear Functions Characterizations of Solution set of Nonsmooth N-Pseudolinear Program Locally Lipschitz N-Pseudolinear Functions and Nonsmooth Vector Optimization Smooth Pseudolinear Functions and Riemannian Manifolds Introduction Definitions and Preliminaries Explicit Formulation of Gradient of Pseudolinear Functions Construction of Pseudolinear Functions Generalizations Pseudolinear Quadratic Fractional Functions Quadratic Fractional Functions Pseudolinearity of Quadratic Fractional Functions and their Characterization Gradient of Pseudolinear Quadratic Fractional Functions Computational Aspect Pseudolinear Fuzzy Mapping Introduction Definitions and Preliminaries Characterizations of Pseudolinear Fuzzy Mappings Characterizations of Solution Sets Numerical Examples Pseudolinear Function and Its Applications Pseudolinear Functions and Hospital Management Pseudolinear Functions and Economics Pseudolinear Functions and Simplex Algorithms