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Nonlinear programming

About: Nonlinear programming is a research topic. Over the lifetime, 19486 publications have been published within this topic receiving 656602 citations. The topic is also known as: non-linear programming & NLP.


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01 Mar 1976
TL;DR: The contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role is supported.
Abstract: It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

338 citations

BookDOI
01 Jan 2004
TL;DR: Daniele et al. as mentioned in this paper studied the strong solvability of a unilateral boundary value problem for nonlinear discontinuous operators in the plane, and the existence of solutions to vector optimization problems.
Abstract: Preface. On the numerical solution of finite-dimensional variational inequalities by an interior point method S. Bellavia, M.G. Gasparo. Fixed points in ordered Banach spaces and applications to elliptic boundary-value problems G. Bonanno, S. Marano. A theorem of the alternative for linear control systems P. Cubiotti. Variational inequalities for static equilibrium market. Lagrangean function and duality P. Daniele. On dynamical equilibrium problems and variational inequalities P. Daniele, A. Maugeri. Nonlinear programming methods for solving optimal control problems C. Durazzi, E. Galligani. Optimal flow pattern in road networks P. Ferrari. On the strong solvability of a unilateral boundary value problem for nonlinear discontinuous operators in the plane S. Giuffre. Most likely traffic equilibrium route flows analysis and computation T. Larsson, et al. Existence of solutions to bilevel variational problems in Banach spaces M.B. Lignola, J. Morgan. On the existence of solutions to vector optimization problems G. Mastroeni, M. Pappalardo. Equilibrium problems and variational inequalities A. Maugeri. Axiomatization for approximate solutions in optimization H. Norde, F. Patrone. Necessary and sufficient conditions of Wardrop type for vectorial traffic equilibria W. Oettli. Approximate solutions and Tikhonov well-posedness for Nash equilibria L.P. Chicco. Equilibrium in time dependent traffic networks with delay F. Raciti. New results on local minima and their applications B. Ricceri. An overview on projection-type methods for convex large-scale quadratic programs V. Ruggiero, L. Zanni.

337 citations

01 Jan 1996
TL;DR: The primal-dual interior point method for linear programming has been shown to be locally and quadratically convergent under only the standard Newton method assumptions in this article, and a global convergence theory for this algorithm has been established.
Abstract: In this work, we first study in detail the formulation of the primal-dual interior-point method for linear programming. We show that, contrary to popular belief, it cannot be viewed.as a damped Newton method applied to the Karush-Kuhn-Tucker conditions for the loga- rithmic barrier function problem. Next, we extend the formulation to general nonlinear programming, and then validate this extension by demonstrating that this algorithm can be implemented so that it is locally and Q-quadratically convergent under only the standard Newton method assumptions. We also establish a global convergence theory for this algorithm and include promising numerical experimentation.

337 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that both linear and nonlinear separation may be achieved by linear programming, and that linear and ellipsoidal separation may also be achieved using nonlinear programming.
Abstract: A pattern separation problem is basically a problem of obtaining a criterion for distinguishing between the elements of two disjoint sets of patterns. The patterns are usually represented by points in a Euclidean space. One way to achieve separation is to construct a plane or a nonlinear surface such that one set of patterns lies on one side of the plane or the surface, and the other set of patterns on the other side. Recently, it has been shown that linear and ellipsoidal separation may be achieved by nonlinear programming. In this work it is shown that both linear and nonlinear separation may be achieved by linear programming.

336 citations

Book
01 Jan 1982
TL;DR: 1. Management Science The Management Science Approach to Problem Solving Model Building: Break-Even Analysis Computer Solution Management Science Modeling Techniques Business Usage of Management Science Techniques Management Science Models in Descision Support Systems
Abstract: 1. Management Science The Management Science Approach to Problem Solving Model Building: Break-Even Analysis Computer Solution Management Science Modeling Techniques Business Usage of Management Science Techniques Management Science Models in Descision Support Systems 2. Linear Programming: Model Formulation and Graphical Solution Model Formulation A Maximization Model Example Graphical Solutions of Linear Programming Methods A Minimization Model Example Irregular Types of Linear Programming Problems Characteristics of Linear Programming Problems 3. Linear Programming: Computer Solution and Sensitivity Analysis Computer Solution Sensitivity Analysis 4. Linear Programming: Modeling Examples A Product Mix Example A Diet Example An Investment Example A Marketing Example A Transportation Example A Blend Example A Multiperiod Scheduling Example A Data Envelopment Analysis Example 5. Integer Programming Integer Programming Models Integer Programming Graphical Solution Computer Solution of Integer Programming Problems with Excel and QM for Windows 0-1 Integer Programming Modeling Examples 6. Transportation, Transshipment, and Assignment Problems The Transportation Model Computer Solution of a Transportation Problem The Transshipment Model The Assignment Model Computer Solution of the Assignment Problem 7. Network Flow Models Network Components The Shortest Route Problem The Minimal Spanning Tree Problem The Maximal Flow Problem 8. Project Management The Elements of Project Management CPM/PERT Probabilistic Activity Times Microsoft Project Project Crashing and Time-Cost Trade-Off Formulating the CPM/PERT Network as a Linear Programming Model 9. Multicriteria Decision Making Goal Programming Graphical Interpretation of Goal Programming Computer Solution of Goal Programming Problems with QM for Windows and Excel The Analytical Hierarchy Process Scoring Model 10. Nonlinear Programming Nonlinear Profit Analysis Constrained Optimization Solution of Nonlinear Programming Problems with Excel A Nonlinear Programming Model with Multiple Constraints Nonlinear Model Examples 11. Probability and Statistics Types of Probability Fundamentals of Probability Statistical Independence and Dependence Expected Value The Normal Distribution 12. Decision Analysis Components of Decision Making Decision Making without Probabilities Decision Making with Probabilities Decision Analysis with Additional Information Utility 13. Queuing Analysis Elements of Waiting Line Analysis The Single-Server Waiting Line System Undefined and Constant Service times Finite Queue Length Finite Calling Population The Multiple-Server Waiting Line Additional Types of Queuing Systems 14. Simulation The Monte Carlo Process Computer Simulation with Excel Spreadsheets Simulation of a Queuing System Continuous Probability Distributions Statistical Analysis of Simulation Results Crystal Ball Verification of the Simulation Model Areas of Simulation Application 15. Forecasting Forecasting Components Time Series Methods Forecast Accuracy Time Series Forecasting Using Excel Time Series Forecasting Using QM for Windows Regression Methods 16. Inventory Management Elements of Inventory Management Inventory Control Systems Economic Order Quantity Models The Basic EOQ Model The EOQ Model with Noninstantaneous Receipt The EOQ Model with Shortages EOQ Analysis with QM for Windows EOQ Analysis with Excel and Excel QM Quantity Discounts Reorder Point Determining Safety Stocks Using Service Levels Order Quantity for a Periodic Inventory System Appendix A Normal Table Chi-Square Table Appendix B Setting Up and Editing a Spreadsheet Appendix C The Poisson and Exponential Distributions Solutions to Selected Odd-Numbered Problems Glossary Index Photo Credits CD-ROM Modules

336 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023113
2022259
2021615
2020650
2019640
2018630