1 edition of **Methods of feasible directions** found in the catalog.

Methods of feasible directions

G. Zoutendijk

- 278 Want to read
- 12 Currently reading

Published
**1960**
by Elsevier
.

Written in English

**Edition Notes**

Statement | by G. Zoutendijk. |

ID Numbers | |
---|---|

Open Library | OL20205202M |

Linear programming was developed during World War II, when a system with we will focus methods of solving them. Section 6 introduces concepts necessary for introducing the called a feasible point and the set of all such points is called the feasible re-gion. Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange.

For the case of multiple resource types, the Q-RAM approach can only generate near-optimal results. In this study, for the formulated radar resource allocation problem with multiple resource types, the Methods of Feasible Directions are considered as an alternative solution by: 1. Our goal is to attain a point satisfying the stationarity necessary optimality condition, defined as the lack of feasible descent directions. Although elementary in smooth optimization, this condition is nontrivial when the objective function is nonsmooth, and, correspondingly, there are very few methods that obtain stationary points in such Cited by: 4.

Abstract: We discuss a finite method of a feasible direction for linear programming problems. The method begins with a feasible basic vector for the problem, constructs a profitable direction to move using the updated column vectors of the nonbasic variables eligible to Cited by: One advantage of these methods over Penalty methods (to be discussed later): We only need to evaluate the function f(x) for points in the feasible region. This can be important if the function is undeﬁned outside the feasible region or if we need to stop early. Example: If f(x) involves taking the log of one of the variables, then theFile Size: 99KB.

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Methods of Feasible Directions: A Study in Linear and Non-Linear Programming by G. Zoutendijk and a great selection of related books, art and collectibles available now at Pironneau, O. and Polak, E. (), Rate of convergence of a class of methods of feasible directions, SIAM Journal on Numerical Analysis, Vol.

10, pp. – MathSciNet CrossRef Google Scholar Polak, E. (), Computational Methods in Optimization, Cited by: 9. Methods of feasible directions; a study in linear and nonlinear programming. [G Zoutendijk] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for The linear programming problem and the methods of feasible direction -- 9.

Quadratic programming -- This paper deals with the rate of convergence of four methods of feasible directions: the Zoutendijk procedures 1 and 2 and two modifications of these procedures due to the authors. Methods of Feasible Directions. Mokhtar S. Bazaraa. Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, Georgia.

Book Author(s): Mokhtar S. Bazaraa. Georgia Institute of Technology, School of Industrial and Systems Engineering, Atlanta, Georgia.

Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study. The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied.

Computers Cited by: tionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed. We also derive a novel sequential linear programming algorithm for generalFile Size: KB. His method can also be used to solve linear equations and equations with non-linear constraints.

As well, other normalization schemes are possible. The reader should consult his (difficult) book for more information. References [1] Zoutendijk, G. Methods of Feasible Directions, A Study in Linear and Non-Linear Programming, Elsevier, Methods of feasible directions;: A study in linear and nonlinear programming Unknown Binding – January 1, by G Zoutendijk (Author) See all formats and editions Hide other formats and editions.

Price New from Used from Author: G Zoutendijk. I assume this refers to mathematical optimization. These problems generally have two components: 1. the objective/cost you want to optimize, and 2. the set/space of parameters over which an algorithm searches for an optimum.

Typically the 2nd comp. In order to find the feasible directions, I proved that any feasible direction has to move the point $(x_1, x_2)$ above the tangent at $(x_1, x_2)$ to the circle, for any positive $\alpha$ (where $\alpha$ comes from the definition of feasible direction).

Feasible directions, global minima, and convex problems. The key fact that we used in the previous developments was that for every, points of the form for sufficiently close to 0 belong to.

This is no longer the case if has a boundary (e.g., is a closed ball in). NONLINEAR PROGRAMMING LECTURE 9: FEASIBLE DIRECTION METHODS LECTURE OUTLINE • Conditional Gradient Method • Gradient Projection Methods A feasible direction at an x ∈ X is a vector d =0 such that x+ αdis feasible for all suff.

small α>0 x1 x2 d Constraint set X Feasible directions at xFile Size: KB. A new method of feasible directions is presented which uses an efficient antizig-zagging scheme. At every iteration, the gradient of the cost function and the gradients of the active constraints Author: Gerard Meyer.

Meyer G.G.L. () Methods of feasible directions with increased gradient memory. In: Stoer J. (eds) Optimization Techniques.

Lecture Notes in Author: Gerard G. Meyer. Feasible Region and Level Curves of the Objective Function: The shaded region in the plot is the feasible region and represents the intersection of the ve inequalities constraining the values of x 1 and x 2.

On the right, we see the optimal solution is the \last" point in the feasible region that intersects a levelFile Size: 2MB. IE Lecture 22 2 Methods of Feasible Directions ‘ In Chapter 9, we looked at methods of using unconstrained optimization techniques on constrained problems. ‘ These methods enforced some of the constraints implicitly.

‘ Now, we look at the methods that explicitly enforce feasibility while ensuring convergence. ‘ Recall the concept of an improving, feasible direction.

Feasibility may refer to. Logical possibility, that which is achievable; Feasible region, a region that satisfies mathematical constraints; Feasibility study, a preliminary study to determine a project's viability "Feasibility Study" (The Outer Limits), an episode of The Outer Limits TV showSee also.

Practicality. The most important results of this study are: 1. the development of a new computational algorithm for the simplex method, which turns out to lead to considerably smaller computer terms than any existing algorithm; 2.

the development of a number of methods for the convex programming problems, called methods of feasible directions, which use the Cited by:.

Methods of Descent for Nondifferentiable Optimization Methods of Descent for Nondifferentiable Optimization. Authors: Kiwiel, Krzysztof C. Free Preview. Buy this book eB09 Methods of feasible directions for nonconvex constrained problems.

Pages De nition (Set of linearized feasible directions F(x)) Given a feasible point x and the active constraint set A(x), F(x) = (p jp satis es (rc i(x)Tp = 0 8i rd j(x)Tp 0 8d j 2A(x)) The set of linearized feasible directions is the best algebraic description available, but in general T (x) ˆF(x) Constraint quali cations are su cient for T (x) = F(x).Usable-feasible direction S Fig.

2. Effect of push-off factor, A, on the direction S. Application of methods of feasible directions to structural optimization problems Equation (8) is, in effect, some sort of penalty function which "pushes harder" as the deisgn becomes closer to the constraint by: 6.