Nonlinear Programming 4

Proceedings of the Nonlinear Programming Symposium 4 Conducted by the Computer Sciences Department at the University of Wisconsin–Madison, July 14-16, 1980

Olvi L. Mangasarian, Robert R. Meyer, Stephen M. Robinson

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780124686625
• eBook ISBN:
  9781483260174
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Nonlinear Programming, 4 focuses on linear, quadratic, and nonlinear programming, unconstrained minimization, nonsmooth and discrete optimization, ellipsoidal methods, linear complementarity problems, and software evaluation. The selection first elaborates on an upper triangular matrix method for quadratic programming, solving quadratic programs by an exact penalty function, and QP-based methods for large-scale nonlinearly constrained optimization. Discussions focus on large-scale linearly constrained optimization, search direction for superbasic variables, finite convergence, basic properties, comparison of three active set methods, and QP-based methods for dense problems. The book then examines an iterative linear programming algorithm based on an augmented Lagrangian and iterative algorithms for singular minimization problems. The publication ponders on the derivation of symmetric positive definite secant updates, preconditioned conjugate gradient methods, and finding the global minimum of a function of one variable using the method of constant signed higher order derivatives. Topics include effects of calculation errors, application to polynomial minimization, using moderate additional storage, updating Cholesky factors, and utilizing sparse second order information. The selection is a valuable source of data for researchers interested in nonlinear programming.

Table of contents

• Front Cover
• Nonlinear Programming 4
• Copyright Page
• Table of Contents
• CONTRIBUTORS
• PREFACE
• CHAPTER 1. AN UPPER TRIANGULAR MATRIX METHOD FOR QUADRATIC PROGRAMMING
• CHAPTER 2. SOLVING QUADRATIC PROGRAMS BY AN EXACT PENALTY FUNCTION
• CHAPTER 3. QP–BASED METHODS FOR LARGE-SCALE NONLINEARLY CONSTRAINED OPTIMIZATION
• CHAPTER 4. NUMERICAL EXPERIMENTS WITH AN EXACT L1 PENALTY FUNCTION METHOD
• CHAPTER 5. AN ITERATIVE LINEAR PROGRAMMING ALGORITHM BASED ON AN AUGMENTED LAGRANGIAN
• CHAPTER 6. ITERATIVE ALGORITHMS FOR SINGULAR MINIMIZATION PROBLEMS
• CHAPTER 7. A NEW DERIVATION OF SYMMETRIC POSITIVE DEFINITE SECANT UPDATES
• CHAPTER 8. ON PRECONDITIONED CONJUGATE GRADIENT METHODS
• CHAPTER 9. FINDING THE GLOBAL MINIMUM OF A FUNCTION OF ONE VARIABLE USING THE METHOD OF CONSTANT SIGNED HIGHER ORDER DERIVATIVES
• CHAPTER 10. ON A BUNDLE ALGORITHM FOR NONSMOOTH OPTIMIZATION
• CHAPTER 11. CONVERGENCE RESULTS IN A CLASS OFVARIABLE METRIC SUBGRADIENT METHODS1
• CHAPTER 12. MONOTROPIC PROGRAMMING: DESCENT ALGORITHMS AND DUALITY
• CHAPTER 13. APPROXIMATION AND CONVERGENCE IN NONLINEAR OPTIMIZATION
• CHAPTER 14. UPPER PLANES OF QUADRATIC 0-1 FUNCTIONS AND STABILITY IN GRAPHS
• CHAPTER 15. ON THE EXISTENCE OF FAST APPROXIMATION SCHEMES
• CHAPTER 16. POLYNOMIALLY BOUNDED ELLIPSOID ALGORITHMS FOR CONVEX QUADRATIC PROGRAMMING
• CHAPTER 17. THE IMPLICIT COMPLEMENTARITY PROBLEM
• CHAPTER 18. METHODS FOR EVALUATING NONLINEAR PROGRAMMING SOFTWARE
• SUBJECT INDEX