Introduction to Applied Optimization

Foreword. Acknowledgements. 1: Introduction. 1.1. Problem Formulation: A Cautionary Note. 1.2. Degrees of Freedom Analysis. 1.3. Objective Function, Constraints, and Feasible Region. 1.4. Numerical Optimization. 1.5. Types of Optimization Problems. 1.6. Summary. 2: Linear Programming. 2.1. The Simplex Method. 2.2. Infeasible Solution. 2.3. Unbounded Solution. 2.4. Multiple Solutions. 2.5. Sensitivity Analysis. 2.6. Other Methods. 2.7. Hazardous Waste Blending Problem as an LP. 2.8. Summary. 3: Nonlinear Programming. 3.1. Convex and Concave Functions. 3.2. Unconstrained NLP. 3.3. Necessary and Sufficient Conditions, and Constrained NLP. 3.4. Sensitivity Analysis. 3.5. Numerical Methods. 3.6. Hazardous Waste Blending: An NLP. 3.7. Summary. 4: Discrete Optimization. 4.1. Tree and Network Representation. 4.2. Branch and Bound for IP. 4.3. Numerical Methods for IP, MILP, and MINLP. 4.4. Probabilistic Methods. 4.5. Hazardous Waste Blending: A Combinatorial Problem. 4.6. Summary.5: Optimization Under Uncertainty. 5.1. Types of Problems and Generalized Representation. 5.2. Chance Constrained Programming Method. 5.3. L-shaped Decomposition Method. 5.4. Uncertainty Analysis and Sampling. 5.5. Stochastic Annealing: An Efficient Algorithm for Combinatorial Optimization under Uncertainty. 5.6. Hazardous Waste Blending under Uncertainty. 5.7. Summary. 6: Multi-objective Optimization. 6.1. Nondominated Set. 6.2. Solution Methods. 6.3. Hazardous Waste Blending and Value of Research: An MOP. 6.4. Summary. 7: Optimal control And Dynamic Optimization. 7.1. Calculus of Variations. 7.2. Maximum Principle. 7.3. Dynamic Programming. 7.4. Stochastic Dynamic Programming. 7.5. Reversal of Blending: Optimizing a Separation Process. 7.6. Summary. Appendix A. Appendix B. Index.