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Tuesday, July 21, 2020 | History

2 edition of **class of variable-metric-secant algorithms for unconstrained minimization** found in the catalog.

class of variable-metric-secant algorithms for unconstrained minimization

Jian Guo

- 324 Want to read
- 28 Currently reading

Published
**1993**
.

Written in English

- Mathematical optimization.,
- Algorithms.

**Edition Notes**

Other titles | Class of variable metric secant algorithms for unconstrained minimization. |

Statement | by Jian Guo. |

The Physical Object | |
---|---|

Pagination | ix, 146 leaves, bound ; |

Number of Pages | 146 |

ID Numbers | |

Open Library | OL14698316M |

This chapter discusses a class of seemingly unrelated methods that attempt to solve the system of equations and inequalities constituting the necessary optimality conditions for the constrained optimization problem. The methods to be used for unconstrained minimization of the augmented Lagrangian rely on the continuity of second derivatives. All algorithms for unconstrained minimization require the user to start from a certain point, so-called the starting point, which we usually denote by x 0. It is good to choose x 0 such that it is a reasonable estimation of the solution. But, to find such estimation, a little more knowledge about the considered set of data is needed, and the.

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in , it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or . Unconstrained minimization of multivariate scalar functions (minimize) The minimize function provides a common interface to unconstrained and constrained minimization algorithms for multivariate scalar functions in demonstrate the minimization function, consider the problem of minimizing the Rosenbrock function of \(N\) variables.

For documentation see Dennis and Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, , and Schnabel, Koontz, and Weiss, "A Modular System of Algorithms for Unconstrained Minimization," ACM Transactions of Mathematical Software, , pages -- solution. In this book we focus on iterative algorithms for the case where X is convex, and fis either convex or is nonconvex but diﬀerentiable. Most of these algorithms involve one or both of the following two ideas, which will be discussed in Sections and , respectively: (a) Iterative descent, whereby the generated sequence {xk} is.

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Variable metric algorithms are a class of algorithms for unconstrained optimization. Consider the unconstrained optimization problem min x ∈ R n f (x). This is a preview of subscription content, log in to check access.

Self-Scaling Variable Metric Algorithms Without Line Search for Unconstrained Minimization* By Shmuel S. Oren Abstract. This paper introduces a new class of quasi-Newton algorithms for uncon-strained minimization in which no line search is necessary and.

BROYDEN, C.G. "The convergence of a class of double rank minimization algorithms" J. Inst. 6,pp–90 and – Google ScholarAuthor: L. Grandinetti. Pod Vodárenskou věží 2, 07 Prague 8 Abstract: A new family of limited-memory variable metric or quasi-Newton methods for unconstrained minimization is given.

Dissertation: A Class of Variable-Metric-Secant Algorithms for Unconstrained Minimization. Advisor: Robert Bill Mifflin. No students known. If you have additional information or corrections regarding this mathematician, please use the update form.

In book: Encyclopedia of indicate that the new method may be preferable to current algorithms for solving many unconstrained minimization problems. The Convergence of a Class of Double. We present a class of algorithms for solving constrained optimization problems.

In the algorithm nonnegatively constrained quadratic programming subproblems are iteratively solved to obtain estimates of Lagrange multipliers and with these estimates a sequence of points which converges to the solution is.

Among the recent unconstrained minimization procedures, quasi-Newton algorithms [4,5] are usually considered to be the most efficient. this book is to provide a unified body of theory on. algorithm phases) Unconstrained minimization 10– Examples • applies to special class of convex functions (‘self-concordant’ functions) • developed to analyze polynomial-time interior-point methods for convex optimization Unconstrained minimization 10– Optimality conditions for unconstrained minimization W e ﬁrst consider what we might deduce if w e were fortunate enough to ha ve found a local minimizer of f (x).

In the last four chapters two basic types of unconstrained minimization algorithms were described in detail.

Specific examples of interior and exterior point algorithms—the logarithmic penalty function, the inverse penalty function, and the quadratic loss function—have been cited.

Obviously many more examples can be generated. Powell, M.J.D. ( b), ‘ On the global convergence of trust region algorithms for unconstrained minimization ’, Math. Program. 29, – Powell, M.J.D. (), ‘ Convergence properties of algorithms for nonlinear optimization ’, Report DAMTP /NA1, Department of Applied Mathematics and Theoretical Physics, University of.

STRAINED MINIMIZATION 33 General line search descent algorithm for unconstrained minimization 33 General structure of a line search descent method. 34 One-dimensional line search 35 Golden section method 36 Powell's quadratic interpolation algorithm 38.

CONVERGENCE PROPERTIES OF A CLASS OF MINIMIZATION ALGORITHMS by M.J.D. Powell 1) ABSTRACT Many iterative algorithms for minimizing a func tion F (x) = F (.,2,x) require first derivative s of F(x) to be calculated, but they maintain an approximation to the second derivative matrix auto matically.

unconstrained minimization (SUM) methods discussed by Fiacco and Mc-Cormick in their classic book [94]. They focus on barrier-function and penalty-function algorithms, in which the auxiliary functions are intro-duced to incorporate the constraint that f is to be minimized over C.

An algorithm is being presented for a special class of unconstrained minimization problems. The algorithm exploits the special structure of the Hessian in the problems under consideration.

It is based on applying Bertsekas' [1] Scaled Partial Conjugate Gradient method with respect to a metric that is updated by the Rank One update, using. these methods is the book by Fiacco and McCormick [12]. The SUMMA [13] is a broad class of sequential unconstrained minimization algorithms that includes barrier-function methods, proximal minimization with Bregman functions [14, 15, 16], the SMART, and, after some reformulation, penalty-function methods.

The choice of the. This paper has two aims: to exhibit very general conditions under which members of a broad class of unconstrained minimization algorithms are globally convergent in a strong sense, and to propose several new algorithms that use second derivative information and achieve such convergence.

In the first part of the paper we present a general trust-region-based algorithm schema that includes an. This book is divided into 13 chapters and begins with a survey of the global and superlinear convergence of a class of algorithms obtained by imposing changing bounds on the variables of the problem.

The succeeding chapters deal with the convergence of the well-known reduced gradient method under suitable conditions and a superlinearly convergent quasi-Newton method for unconstrained minimization.

This paper extends the known excellent global convergence properties of trust region algorithms for unconstrained optimization to the case where bounds on the variables are present.

Weak conditions on the accuracy of the Hessian approximations are considered. It is also shown that, when the strict complementarily condition holds, the proposed algorithms reduce to an unconstrained calculation.

To calculate we could follow Marquardt (), and define _8' ' to minimize expression (13) subject to condition (14). But in this c a s e the condition (14) may n e c e s s i t a t e of order n 3 computer operations, which is not acceptable because most other algorithms for unconstrained minimization use only of order n operations per iteration.Abstract.

This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches, it is shown that under appropriate assumptions on the function to be, minimized and stated conditions on the line search each algorithm in this class converges globally and superlinearly on convex functions.Although the focus is on methods, it is necessary to learn the theoretical properties of the problem and of the algorithms designed to solve it.

Work for the course will include: 4 homeworks. A project where you code an optimization algorithm. A final exam. Download the full syllabus here. Time & Location.