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Topic: Feasible region

	Insights Into Algebra 1 . Workshop 3
		The shaded region is called the feasible region because it represents all the possible points that satisfy the system of inequalities.
		The optimum point is located on a corner of the feasible region (or the intersection of two of the boundary lines), and its coordinates are usually integer values.
		Each point in the feasible region represents a possible combination of telemark skis and cross-country skis that the manufacturer can produce and satisfy both constraints.
	www.learner.org /channel/workshops/algebra/workshop3/index2.html (1168 words)

	[No title]
		Represent the general solution (point in the feasible region) of this problem in terms of the extreme points and direction vectors.
		Is the feasible region in your graph a polyhedron?
		Describe or sketch on paper the conical hull of the feasible region.
	www.saintmarys.edu /~cpeltier/Math438F04/Activities/438ACT8.doc (489 words)

	[No title]
		A feasible solution is an assignment of values to the decision variables that satisfies all the problem's constraints.
		An optimal solution is a feasible solution that results in the largest possible objective function value, z, when maximizing or smallest z when minimizing¡P 2¥Wó¨Graphical Solutions¨éPlot all constraints including nonnegativity ones Determine the feasible region.
		Assuming that a feasible region exists, an optimal solution will always occur at one or more of the extreme points, where an extreme point is a corner point of the feasible region.
	myweb.lmu.edu /lleon/mbaa607/LPSolutions.ppt (1463 words)

	The Simplex Method
		At each iteration of the simplex method, the algorithm starts at one vertex of the feasible region and moves along an edge to the next vertex.
		The feasible region is the set of points that satisfies all of the constraints.
		We are interested in vertices of the feasible region, and these solutions correspond to basic solutions of the linear system.
	www-fp.mcs.anl.gov /otc/Guide/CaseStudies/Simplex/feasible.html (746 words)

	Graphical Approach to Linear Programming
		We know that the optimal solution will occur at one of the extreme points (corners of the feasible region), but we need to identify which extreme point will be best.
		For this example, when the objective function value is 6, the line goes through the feasible region; therefore, it is possible to make at least 6 units of profit.
		The line corresponding to 12 units of profit also goes through the feasible region; therefore, it is possible to find a feasible solution that results in 12 units of profit.
	www.ngcsu.edu /Academic/Bus_Gov/BADM/kmelton/LPgraph.htm (844 words)

	[No title]
		The major ideas introduced are the notions of a basic solution and basic feasible solution, basis matrix and basic variables, which are essential to understanding the simplex algorithm.
		Note that the set of basic feasible solutions is the same as the set of extreme points of the feasible region for the standard form of the problem.
		Identify feasible basic solutions Determine which of the points from 3 are in the feasible region 5.
	www.saintmarys.edu /~cpeltier/Math438F04/Activities/438ACT10.doc (800 words)

	Linearly Constrained Global Optimization
		The parametric representation of the feasible region with parameters
		The parametric representation of the interior of the feasible region is:
		Therefore, the feasible region is indeed an unbounded one.
	home.ubalt.edu /ntsbarsh/opre640a/nonlinear.htm (9314 words)

	Branch and Bound
		There must also be a way to compute an upper bound (feasible solution) for at least some instances; for practical purposes, it should be possible to compute upper bounds for some set of nontrivial feasible regions.
		Otherwise, the feasible region is divided into two or more regions, each strict subregions of the original, which together cover the whole feasible region; ideally, these subproblems partition the feasible region.
		Since it is feasible, it can be used to prune the rest of the tree: if the lower bound for a node exceeds the best known feasible solution, no globally optimal solution can exist in the subspace of the feasible region represented by the node.
	www.cs.sandia.gov /opt/survey/branch-and-bound.html (318 words)

	Graphical Solutions of LP
		Along with the non-negativity restrictions on the decision variables, the intersection of the half-spaces defined by these constraints is the feasible region shown in blue.
		And since all of the contours, or level curves of the objective function are parallel and perpendicular to the gradient, it is a simple matter to superimpose both of these items on the sketch of the feasible region, as we have done in Figure II.3 for the sample problem.
		Just stating that the Simplex Method is an exterior point method is not a strong enough statement to reveal why the search traverses only the edges of the feasible region polyhedron and why it doesn't occasionally jump off into the infeasible region as it moves from corner to corner.
	www.dean.usma.edu /math/courses/ma481/graphlp1.htm (1635 words)

	Chapter 4
		But if all the original decision variables are set to zero (we are at the origin) and the slack variables take on their largest possible values (40, 30, and 15), then we have at least one solution.
		Because most of the solutions correspond to being in the interior of the feasible region, or in the exterior of the feasible region, not on the boundary where the corner points are located.
		Here is a table of all the basic feasible solutions and their corresponding corner points.
	euphrates.wpunj.edu /faculty/rieperr/chap4.html (641 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		(B) If the feasible region is unbounded, and the coefficients of the objective function are positive, then the minimum value of the objective function exists, but the maximum value does not.
		(C) If the feasible region is empty (that is, there are no points that satisfy all the constraints), the both the maximum value and the minimum value of the objective function do not exist.
		The feasible region S is the solution set of the given inequalities, and is indicated by the shading in the graph at the right.
	www.nccu.edu /artsci/math/melikyan/mat_fm/lec/lec5_2.ppt (872 words)

	Feasible Region Calculus
		Of particular interest is the derivation of regions, defined in the state space of aggregate metrics, that imply satisfaction of all individual temporal performance constraints.
		We are also interested in developing a calculus for composing feasible regions of arbitrary topology software systems.
		The computation of such regions allows computation of overall capacity of large systems (their ability to meet deadlines) as well as performance optimization of large software components subject to timeliness constraints.
	www.cs.uiuc.edu /homes/zaher/qos/theory.html (529 words)

	Generalization to the n-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear ...
		Generalization to the n-var case: the ``geometry'' of the LP feasible region and the Fundamental Theorem of Linear Programming
		In this section we generalize the geometry of the 2-var LP's, presented in the previous section, to LP's with n decision variables.
		The study of the ``geometric'' properties of the LP feasible region for this general case, will eventually lead to the Fundamental Theorem of Linear Programming, which is at the basis of the Simplex algorithm.
	www2.isye.gatech.edu /~spyros/LP/node13.html (106 words)

	Active Set Methods
		If the feasible region G is empty, no solution to the optimization problem exists.
		If you cannot expect an improvement in the value of the objective function by moving from an active constraint back into the interior of the feasible region, you use this inequality constraint as an equality constraint in the next iteration.
		Otherwise you release the active inequality constraint and increase the dimension of the optimization problem in the next iteration.
	www.asu.edu /sas/sasdoc/sashtml/ormp/chap5/sect32.htm (738 words)

	Feasible Offset Region Based Tool Path Planning for Face Milling
		Ramachandran, P., “Feasible Offset Region Based Tool Path Planning for Face Milling", 2002-2003 LMA Reports, University of California at Berkeley, pp.
		This report describes the optimization of tool path plans to minimize burr formation while face milling powertrain components in the automotive industry.
		The algorithm controls conditions responsible for burr formation by manipulating tool offsets to generate a feasible region for selection of tool paths.
	repositories.cdlib.org /lma/codef/2002_ramachandran (140 words)

	Active Set Methods
		The m linear constraints define a feasible region G in R
		never leaves the feasible region G of the optimization problem, but it can reach its boundaries.
		If the algorithm cannot improve the value of the objective function by moving from an active constraint back into the interior of the feasible region, it makes this inequality constraint an equality constraint in the next iteration.
	www.asu.edu /sas/sasdoc/sashtml/stat/chap46/sect28.htm (657 words)

	[No title]
		Note that in (b) the feasible region is unbounded and the objective function line can be moved parallel to itself without bound so that z can be increased infinitely.
		NOTE: The feasible region in this problem is limited to a single point.
		An unbounded feasible region might not result in an unbounded solution for a minimization or maximization problem.
	www.swlearning.com /quant/asw/qmb_9e/sg_ch07.doc (2310 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		That is, we can determine the feasibility of a basic solution simply by examining the signs of all the variables in the solution.
		If a basic solution has no negative values, it is a basic feasible solution.
		But it is an important step in that we have been able to identify all the corner points (vertices) of the feasible set without drawing its graph since the graphical method will not work for systems having 3 or more variables.
	www.nccu.edu /artsci/math/melikyan/mat_fm/lec/lec5_3.ppt (1825 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Thus, x* must be a vertex of A.¡@? çÿ çÿó+¨The SIMPLEX Algorithm¨¨Lets convert the linear program to its slack form Basic feasible solution: all non-basic variables are set to 0 and the basic variables are set by the constraints.¡©Z©ó1¨The SIMPLEX Algorithm¨§Pivoting: replace a non-basic entering variable with a basic leaving variable.
		It determines if the LP is feasible and returns the slack form for which the initial basic solution is feasible.
		When the feasible region is empty.¡(5Nð¦² ð00 óðZA"¡?A¿ÀÅAÿ ?°ðÀ ðÁ¡Ãr ðÚ¢ ð0 ð0Àå) ¿¿ÀÿðÐ °d ðz H(0,0) doesn t satisfy the constraint¡% 2%ðX2 ð0 ð0¿ÀÿðÐ`à ðH ð0 ð0“”Þ½h¿ÿ ?ð ÿÿÿ___ff3ÌÌÌÌff²²²‘º___PPT10ië.NáÅ kÈ»+Dñ='ñ 4ÿÿÿÿ=ñ @Bñ +îUï ! 0 lðdÀð
	www.cs.technion.ac.il /~reuven/APPROX-SEMINAR/spr06/lp.ppt (521 words)

	feasible solution (Site not responding. Last check: 2007-11-02)
		Definition: Any element of the feasible region of an optimization problem.
		Note: From Algorithms and Theory of Computation Handbook, page 34-17, Copyright © 1999 by CRC Press LLC.
		Algorithms and Theory of Computation Handbook, CRC Press LLC, 1999, "feasible solution", in Dictionary of Algorithms and Data Structures [online], Paul E. Black, ed., U.S. National Institute of Standards and Technology.
	www.nist.gov /dads/HTML/feasiblesltn.html (109 words)

	Feasible Region Approximation Using Convex Polytopes (ResearchIndex) (Site not responding. Last check: 2007-11-02)
		If your firewall is blocking outgoing connections to port 3125, you can use these links to download local copies.
		Abstract: A new technique for polytope approximation of the feasible region for a design is presented.
		@inproceedings{ sapatnekar93feasible, author = "Sachin S. Sapatnekar and Pravin M. Vaidya and S. Kang", title = "Feasible Region Approximation Using Convex Polytopes", booktitle = "{ISCAS}", pages = "1786-1789", year = "1993", url = "citeseer.ist.psu.edu/622140.html" }
	citeseer.ist.psu.edu /622140.html (186 words)

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