Sequential quadratic programming

About: Sequential quadratic programming is a research topic. Over the lifetime, 4709 publications have been published within this topic receiving 135463 citations.

Engineering Optimization : Theory and Practice

Abstract: Preface. 1 Introduction to Optimization. 1.1 Introduction. 1.2 Historical Development. 1.3 Engineering Applications of Optimization. 1.4 Statement of an Optimization Problem. 1.5 Classification of Optimization Problems. 1.6 Optimization Techniques. 1.7 Engineering Optimization Literature. 1.8 Solution of Optimization Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 2 Classical Optimization Techniques. 2.1 Introduction. 2.2 Single-Variable Optimization. 2.3 Multivariable Optimization with No Constraints. 2.4 Multivariable Optimization with Equality Constraints. 2.5 Multivariable Optimization with Inequality Constraints. 2.6 Convex Programming Problem. References and Bibliography. Review Questions. Problems. 3 Linear Programming I: Simplex Method. 3.1 Introduction. 3.2 Applications of Linear Programming. 3.3 Standard Form of a Linear Programming Problem. 3.4 Geometry of Linear Programming Problems. 3.5 Definitions and Theorems. 3.6 Solution of a System of Linear Simultaneous Equations. 3.7 Pivotal Reduction of a General System of Equations. 3.8 Motivation of the Simplex Method. 3.9 Simplex Algorithm. 3.10 Two Phases of the Simplex Method. 3.11 MATLAB Solution of LP Problems. References and Bibliography. Review Questions. Problems. 4 Linear Programming II: Additional Topics and Extensions. 4.1 Introduction. 4.2 Revised Simplex Method. 4.3 Duality in Linear Programming. 4.4 Decomposition Principle. 4.5 Sensitivity or Postoptimality Analysis. 4.6 Transportation Problem. 4.7 Karmarkar's Interior Method. 4.8 Quadratic Programming. 4.9 MATLAB Solutions. References and Bibliography. Review Questions. Problems. 5 Nonlinear Programming I: One-Dimensional Minimization Methods. 5.1 Introduction. 5.2 Unimodal Function. ELIMINATION METHODS. 5.3 Unrestricted Search. 5.4 Exhaustive Search. 5.5 Dichotomous Search. 5.6 Interval Halving Method. 5.7 Fibonacci Method. 5.8 Golden Section Method. 5.9 Comparison of Elimination Methods. INTERPOLATION METHODS. 5.10 Quadratic Interpolation Method. 5.11 Cubic Interpolation Method. 5.12 Direct Root Methods. 5.13 Practical Considerations. 5.14 MATLAB Solution of One-Dimensional Minimization Problems. References and Bibliography. Review Questions. Problems. 6 Nonlinear Programming II: Unconstrained Optimization Techniques. 6.1 Introduction. DIRECT SEARCH METHODS. 6.2 Random Search Methods. 6.3 Grid Search Method. 6.4 Univariate Method. 6.5 Pattern Directions. 6.6 Powell's Method. 6.7 Simplex Method. INDIRECT SEARCH (DESCENT) METHODS. 6.8 Gradient of a Function. 6.9 Steepest Descent (Cauchy) Method. 6.10 Conjugate Gradient (Fletcher-Reeves) Method. 6.11 Newton's Method. 6.12 Marquardt Method. 6.13 Quasi-Newton Methods. 6.14 Davidon-Fletcher-Powell Method. 6.15 Broyden-Fletcher-Goldfarb-Shanno Method. 6.16 Test Functions. 6.17 MATLAB Solution of Unconstrained Optimization Problems. References and Bibliography. Review Questions. Problems. 7 Nonlinear Programming III: Constrained Optimization Techniques. 7.1 Introduction. 7.2 Characteristics of a Constrained Problem. DIRECT METHODS. 7.3 Random Search Methods. 7.4 Complex Method. 7.5 Sequential Linear Programming. 7.6 Basic Approach in the Methods of Feasible Directions. 7.7 Zoutendijk's Method of Feasible Directions. 7.8 Rosen's Gradient Projection Method. 7.9 Generalized Reduced Gradient Method. 7.10 Sequential Quadratic Programming. INDIRECT METHODS. 7.11 Transformation Techniques. 7.12 Basic Approach of the Penalty Function Method. 7.13 Interior Penalty Function Method. 7.14 Convex Programming Problem. 7.15 Exterior Penalty Function Method. 7.16 Extrapolation Techniques in the Interior Penalty Function Method. 7.17 Extended Interior Penalty Function Methods. 7.18 Penalty Function Method for Problems with Mixed Equality and Inequality Constraints. 7.19 Penalty Function Method for Parametric Constraints. 7.20 Augmented Lagrange Multiplier Method. 7.21 Checking the Convergence of Constrained Optimization Problems. 7.22 Test Problems. 7.23 MATLAB Solution of Constrained Optimization Problems. References and Bibliography. Review Questions. Problems. 8 Geometric Programming. 8.1 Introduction. 8.2 Posynomial. 8.3 Unconstrained Minimization Problem. 8.4 Solution of an Unconstrained Geometric Programming Program Using Differential Calculus. 8.5 Solution of an Unconstrained Geometric Programming Problem Using Arithmetic-Geometric Inequality. 8.6 Primal-Dual Relationship and Sufficiency Conditions in the Unconstrained Case. 8.7 Constrained Minimization. 8.8 Solution of a Constrained Geometric Programming Problem. 8.9 Primal and Dual Programs in the Case of Less-Than Inequalities. 8.10 Geometric Programming with Mixed Inequality Constraints. 8.11 Complementary Geometric Programming. 8.12 Applications of Geometric Programming. References and Bibliography. Review Questions. Problems. 9 Dynamic Programming. 9.1 Introduction. 9.2 Multistage Decision Processes. 9.3 Concept of Suboptimization and Principle of Optimality. 9.4 Computational Procedure in Dynamic Programming. 9.5 Example Illustrating the Calculus Method of Solution. 9.6 Example Illustrating the Tabular Method of Solution. 9.7 Conversion of a Final Value Problem into an Initial Value Problem. 9.8 Linear Programming as a Case of Dynamic Programming. 9.9 Continuous Dynamic Programming. 9.10 Additional Applications. References and Bibliography. Review Questions. Problems. 10 Integer Programming. 10.1 Introduction 588. INTEGER LINEAR PROGRAMMING. 10.2 Graphical Representation. 10.3 Gomory's Cutting Plane Method. 10.4 Balas' Algorithm for Zero-One Programming Problems. INTEGER NONLINEAR PROGRAMMING. 10.5 Integer Polynomial Programming. 10.6 Branch-and-Bound Method. 10.7 Sequential Linear Discrete Programming. 10.8 Generalized Penalty Function Method. 10.9 Solution of Binary Programming Problems Using MATLAB. References and Bibliography. Review Questions. Problems. 11 Stochastic Programming. 11.1 Introduction. 11.2 Basic Concepts of Probability Theory. 11.3 Stochastic Linear Programming. 11.4 Stochastic Nonlinear Programming. 11.5 Stochastic Geometric Programming. References and Bibliography. Review Questions. Problems. 12 Optimal Control and Optimality Criteria Methods. 12.1 Introduction. 12.2 Calculus of Variations. 12.3 Optimal Control Theory. 12.4 Optimality Criteria Methods. References and Bibliography. Review Questions. Problems. 13 Modern Methods of Optimization. 13.1 Introduction. 13.2 Genetic Algorithms. 13.3 Simulated Annealing. 13.4 Particle Swarm Optimization. 13.5 Ant Colony Optimization. 13.6 Optimization of Fuzzy Systems. 13.7 Neural-Network-Based Optimization. References and Bibliography. Review Questions. Problems. 14 Practical Aspects of Optimization. 14.1 Introduction. 14.2 Reduction of Size of an Optimization Problem. 14.3 Fast Reanalysis Techniques. 14.4 Derivatives of Static Displacements and Stresses. 14.5 Derivatives of Eigenvalues and Eigenvectors. 14.6 Derivatives of Transient Response. 14.7 Sensitivity of Optimum Solution to Problem Parameters. 14.8 Multilevel Optimization. 14.9 Parallel Processing. 14.10 Multiobjective Optimization. 14.11 Solution of Multiobjective Problems Using MATLAB. References and Bibliography. Review Questions. Problems. A Convex and Concave Functions. B Some Computational Aspects of Optimization. B.1 Choice of Method. B.2 Comparison of Unconstrained Methods. B.3 Comparison of Constrained Methods. B.4 Availability of Computer Programs. B.5 Scaling of Design Variables and Constraints. B.6 Computer Programs for Modern Methods of Optimization. References and Bibliography. C Introduction to MATLAB(R) . C.1 Features and Special Characters. C.2 Defining Matrices in MATLAB. C.3 CREATING m-FILES. C.4 Optimization Toolbox. Answers to Selected Problems. Index .

SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization

Abstract: Sequential quadratic programming (SQP) methods have proved highly effective for solving constrained optimization problems with smooth nonlinear functions in the objective and constraints. Here we consider problems with general inequality constraints (linear and nonlinear). We assume that first derivatives are available and that the constraint gradients are sparse. We discuss an SQP algorithm that uses a smooth augmented Lagrangian merit function and makes explicit provision for infeasibility in the original problem and the QP subproblems. SNOPT is a particular implementation that makes use of a semidefinite QP solver. It is based on a limited-memory quasi-Newton approximation to the Hessian of the Lagrangian and uses a reduced-Hessian algorithm (SQOPT) for solving the QP subproblems. It is designed for problems with many thousands of constraints and variables but a moderate number of degrees of freedom (say, up to 2000). An important application is to trajectory optimization in the aerospace industry. Numerical results are given for most problems in the CUTE and COPS test collections (about 900 examples).

Trust Region Methods

Abstract: Preface 1. Introduction Part I. Preliminaries: 2. Basic Concepts 3. Basic Analysis and Optimality Conditions 4. Basic Linear Algebra 5. Krylov Subspace Methods Part II. Trust-Region Methods for Unconstrained Optimization: 6. Global Convergence of the Basic Algorithm 7.The Trust-Region Subproblem 8. Further Convergence Theory Issues 9. Conditional Models 10. Algorithmic Extensions 11. Nonsmooth Problems Part III. Trust-Region Methods for Constrained Optimization with Convex Constraints: 12. Projection Methods for Convex Constraints 13. Barrier Methods for Inequality Constraints Part IV. Trust-Region Mewthods for General Constained Optimization and Systems of Nonlinear Equations: 14. Penalty-Function Methods 15. Sequential Quadratic Programming Methods 16. Nonlinear Equations and Nonlinear Fitting Part V. Final Considerations: Practicalities Afterword Appendix: A Summary of Assumptions Annotated Bibliography Subject and Notation Index Author Index.