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Topic: Simplex algorithm

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	PlanetMath: simplex algorithm
		The simplex algorithm is used as part of the simplex method (due to George B. Dantzig) to solve linear programming problems.
		The simplex algorithm is used as one phase of the simplex method.
		This is version 19 of simplex algorithm, born on 2003-04-24, modified 2006-10-30.
	planetmath.org /encyclopedia/SimplexAlgorithm.html (310 words)

	Linear Programming, Polyhedra, and The Simplex Algorithm (Site not responding. Last check: 2007-10-25)
		To solve a linear programming problem, the simplex algorithm starts at an arbitrary vertex of G and then greedily follows a directed path in G up to the local minimum, the sink, which happens to be the global minimum as well.
		Different variants of the simplex algorithm are obtained by applying different local greedy choices when building the path.
		While linear programming is solvable in polynomial time in the worst case (using the ellipsoid or the interior method), no variant of the simplex algorithm has been shown to run in polynomial time in the worst case.
	facweb.cs.depaul.edu /research/TheorySeminar/abstract102105.htm (283 words)

	Simplex algorithm - Wikipedia, the free encyclopedia
		In both cases, the method uses the concept of a simplex, which is a polytope of N + 1 vertices in N dimensions: a line segment on a line, a triangle on a plane, a tetrahedron in three-dimensional space and so forth.
		The simplex algorithm begins at a starting vertex and moves along the edges of the polytope until it reaches the vertex of the optimum solution.
		Since the simplex algorithm is concerned only with finding a single optimal point (even if other equally-optimal points exist), it is possible to look solely at moves skirting the edge of a simplex, ignoring the interior.
	en.wikipedia.org /wiki/Simplex_algorithm (1206 words)

	Dr. Dobb's \| Simplex Optimization \| October 1, 2003
		Often overlooked, simplex optimization is a reasonable and quick-to-implement solution, useful at least for the initial stages of rapid development and for testing methodologies.
		Simplex just walks around in a stylized way, and you are guaranteed that you will at least have the best answer you have ever stumbled upon.
		The simplex optimization method begins with an initial (often guessed) point (that is, a set of parameter values) and constructs a simplex near that guessed point.
	www.ddj.com /184401716?pgno=6 (1955 words)

	GAUL: Genetic Algorithm Utility Library
		The simplex algorithm is commonly applied to solve linear programming problems.
		One restriction of the simplex algorithm is that the chromosome must be mapped onto a double-precision floating-point array.
		A couple of examples using the simplex search are distributed with GAUL, including fitting_simplex.c which attempts to fit an equation of the form y = Ax exp{Bx+C} + D to an arbitrary dataset, by selecting appropriate values for the parameters A, B, C and D. Home
	gaul.sourceforge.net /tutorial/simplex.html (362 words)

	Nanocell Optimization Techniques
		The Nelder-Mead Simplex algorithm, also known as the Amoeba Algorithm, is based on a simplex algorithm and is used to for minimization or maximization of a multidimensional function.
		These features allow the simplex algorithm to quickly reach the area of the minimum by increasing the volume of the simplex, and then to efficiently find the optimal point by decreasing the volume of the simplex and therefore the breadth of the search near a minimum.
		In this version of the amoeba algorithm, there are several constants that may be changed in order to vary the efficiency and correctness of the results of the algorithm.
	www.cs.duke.edu /~rodger/curious/pages/dolinsky/opt.html (1847 words)

	Egwald Operations Research - Linear Programming - Dual Simplex Algorithm
		The dual simplex method is often used in situations where the primal problem has a number of equality constraints generating artificial variables in the l.p.
		In the dual simplex algorithm, a sequence of tableaux are calculated.
		The dual simplex algorithm terminates, since all conditions of Phase I and II are satisfied.
	www.egwald.com /operationsresearch/lpdualsimplex.php (1198 words)

	Egwald Operations Research - Linear Programming - Simplex Algorithm (Site not responding. Last check: 2007-10-25)
		In the primal simplex algorithm, a sequence of tableaux are calculated.
		The primal simplex algorithm terminates without proceeding to Phase II, since all conditions of Phase I and II are satisfied.
		Similar to the Basic Simplex Algorithm: try to increase the value of P = µ by obtaining nonnegative entries in Ø (the last row) for the sign-restricted primal and slack variables.
	www.egwald.com /operationsresearch/lpsimplex.php (2441 words)

	2. Methods
		The BSSA algorithm is a modification of the downhill simplex (DS) algorithm, which is originally due to Nelder and Mead [11].
		After the preceding series of move attempts has been made, in which the simplex may have moved as many as 3 times, the process is repeated until a convergence criterion is met or the maximum specified number of iterations is achieved.
		The BSSA algorithm was developed as a general scheme for optimizing many-dimensional functions with multiple minima [5].
	www.cooper.edu /engineering/chemechem/ECCC3/methods.html (2252 words)

	Simplex Algorithm
		The Simplex Algorithm (click to see a graphical example of its application) provides an efficient method for refining N and K values for the film (and the substrate if appropriate).
		The measure of deviation is taken to be the mean square deviation of the data from the "closest" points on a constant-index growth curve.
		The Simplex algorithm provides a better approach to the analysis of data on anisotropic films, and has the added advantage that it can deal with oxides that break down before the end of the first cycle.
	www.kw.igs.net /~jackord/ee/e9.html (1240 words)

	PDL::Opt::Simplex -- Simplex optimization routines (Site not responding. Last check: 2007-10-25)
		The basic idea of the algorithm is to move a ``simplex'' of N+1 points in the N-dimensional search space according to certain rules.
		The main benefit of the algorithm is that you do not need to calculate the derivatives of your function.
		Use genetic algorithms or simulated annealing or conjugate gradient or momentum gradient descent.
	pdl.sourceforge.net /PDLdocs/Opt/Simplex.html (308 words)

	The Amoeba algorithm
		On the other hand, the theoretical underpinnings of the algorithm, such as its convergence properties, are less than satisfactory [10, 13].
		In this paper, we focus on one implementation of the Nelder-Mead algorithm as described in the popular handbook Numerical Recipes [17], where it is called the amoeba algorithm.
		The amoeba algorithm maintains at each iteration a nondegenerate simplex, a geometric figure in n dimensions of nonzero volume that is the convex hull of n+1 vertices,
	www.research.ibm.com /infoecon/paps/html/amec99_bundle/node8.html (329 words)

	BUS 202 Quantitative Applications (Site not responding. Last check: 2007-10-25)
		In its bare essentials the simplex algorithm is a search method that systematically searches the corners of the feasible solution for an optimal one.
		In the simplex algorithm each BFS is represented by a simplex table that contains information necessary (1)for the testing of the adjacent BFS for improvement; and (2) generating the simplex table that represents the adjacent BFS that offers improvement.
		This is a process called PIVOT (a math operation) which takes the simplex algorithm from one BFS to an adjacent one.
	www.wfu.edu /~akinc/bus202/simplex.html (499 words)

	The Revised Simplex Method on a GPU
		Various algorithms were implemented to work around this problem wherever it occurred to allow matrix operations to operate on all input sizes.
		The revised simplex is similar to the simplex method, except that matrix inversion is avoided by directly working with inverted matrices throughout the entire process.
		Pseudo code and a flowchart describing the revised simplex algorithm are available, with a somewhat more thorough description given in the report.
	www.cs.sun.ac.za /~ggreeff (1317 words)

	The Simplex Algorithm
		Such a systematic approach is provided by the Simplex algorithm.
		The basic logic of the algorithm is depicted in Figure 12.
		It is also interesting to examine the geometrical interpretation of the behavior of Simplex algorithm.
	www.isye.gatech.edu /~spyros/LP/node22.html (494 words)

	iTOUGH2 Minimization Algorithms
		The purpose of the minimization algorithm is to detect the minimum of the objective function in the n-dimensional parameter space.
		The downhill simplex method requires only function evaluations (i.e., no derivatives) and is therefore a robust but inefficient minimization method.
		Starting with a simplex consisting of n+1 points in the n-dimensional parameter space, a series of steps is taken, most of which just moving the point of the simplex with the highest objective function through the opposite face of the simplex to a lower point.
	esd.lbl.gov /ITOUGH2/Minimization/minalg.html (514 words)

	The modified simplex method
		The modified simplex method has much in common with the basic method, but can adjust its shape and size depending of the response in each step.
		The procedures for expansion and contraction enable the modified simplex both to accelerate along a successful track of improvement and to home in on the optimum conditions.
		The calculations in the MultiSimplex modified simplex algorithm are outlined in the flow chart.
	www.multisimplex.com /simplex_m.htm (371 words)

	Simplex algorithm method - Wikipedia, the free encyclopedia
		This article deals with one of many methods for solving a linear programming problem using the simplex algorithm.
		For a formal definition of the method and an explanation of why it works, refer to the simplex algorithm page.
		This application of the simplex algorithm uses tables, called tableaux, to represent calculations and intermediate steps to completing a problem.
	en.wikipedia.org /wiki/Simplex_algorithm_method (640 words)

	The basic simplex method
		The shapes of the simplex in a one, a two and a three variable search space, are a line, a triangle or a tetrahedron.
		The reevaluation rule avoids the simplex to be stuck around a false favorable response.
		The calculations in the MultiSimplex basic simplex algorithm are outlined in the flow chart.
	www.multisimplex.com /simplex_b.htm (419 words)

	Towards the Simplex Method
		However, each tableau in the simplex method corresponds to a movement from one basic variable set BVS (extreme or corner point) to another, making sure that the objective function improves at each iteration until the optimal solution is reached.
		The simplex method always starts at the origin (which is a corner point) and then jumps from a corner point to the neighboring corner point until it reaches the optimal corner point (if bounded).
		Numerical Recipes states that the Simplex algorithm is 'almost always' O(max(N,M)), which means that the number of iteration is a factor of number of variables or number of constraints, whichever is larger.
	home.ubalt.edu /ntsbarsh/opre640A/partIV.htm (3027 words)

	Overview of the Simplex Algorithm
		In this section we describe briefly a generalized version of the algorithm.
		If this line goes through the investigated simplex, then the line has two intersection points with the surface of this simplex and the inner part of the line represents a segment of the result in the
		This operation has to be repeated for each simplex in the investigated phase space.
	www.fsz.bme.hu /~szebi/papers/europvm99/node2.html (222 words)

	PROC NETFLOW
		Another class of optimization algorithm, the Interior Point algorithm, has been implemented in PROC NETFLOW and can be used as an alternative to the Simplex algorithm to solve network problems.
		The Simplex algorithm, developed shortly after World War II, was the main method used to solve Linear Programming problems.
		More recently, Interior Point algorithms have evolved to become superior to the Simplex algorithm, in general, especially when the problems are large.
	www.asu.edu /sas/sasdoc/sashtml/ormp/chap1/sect4.htm (867 words)

	linprog :: Functions (Optimization Toolbox)
		The large-scale method is based on LIPSOL (Linear Interior Point Solver, [3]), which is a variant of Mehrotra's predictor-corrector algorithm ([2]), a primal-dual interior-point method.
		The first stage of the algorithm might involve some preprocessing of the constraints (see Large-Scale Linear Programming).
		Once the preprocessing has finished, the iterative part of the algorithm begins until the stopping criteria are met.
	www.mathworks.com /access/helpdesk/help/toolbox/optim/ug/linprog.html (1009 words)

	A Fast Algorithm for Functional Mapping of Complex Traits -- Zhao et al. 167 (4): 2133 -- Genetics
		of using the simplex algorithm as an alternative to solve the
		The results from the simplex algorithm are consistent with those
		The Nelder-Mead simplex algorithm, originally proposed by N
	www.genetics.org /cgi/content/full/167/4/2133 (2296 words)

	Java 3D Simplex Tutorial
		The Java 3D Simplex Tutorial is an educational tool for exploring the simplex method, a key topic in linear optimizations.
		The purpose of the tool is allow students to explore the algorithm visually and numerically without being burdened by tedious calculations.
		After adding constraints and setting the objective, the user starts the simplex method by adding artificial variables and initializing an auxilary objective to the sum of the artificials.
	www.duke.edu /~cjj1/simplex (401 words)

	Algorithm Animation: Affine Scaling (Site not responding. Last check: 2007-10-25)
		Since most people benefit greatly from geometric intuition, it is natural to try to represent a algorithms graphically.
		The obvious/textbook graphical representation of algorithms for linear programming involve restricting ones attention to situations with at most 3 variables.
		As the algorithm progresses from an initial solution to the optimal solution, there are times when beams one or both of the tension/compression components of the force are given negative values.
	www.princeton.edu /~rvdb/JAVA/twophase_animate/index.html (495 words)

	Downhill Simplex Algorithm, section 10.4 - Numerical Recipes Forum
		I coded the Nelder Mead simplex method on my Apple II in basic years ago, it is a cool algorithm.
		The idea is to evaluate your function at 3 points, this forms your simplex, one of the three points will be the largest (of those 3) functional value.
		From that point you draw a line through the mid point of the opposite side of the triangle, your next point to sample will be on this line.
	www.nr.com /forum/showthread.php?p=798 (380 words)

	The Simplex Method (Site not responding. Last check: 2007-10-25)
		The simplex method was the first method developed to solve linear programs.
		Users can select the size of the problem that they want to solve (up to 7 variables and 7 constraints), enter the data, and watch the simplex method go through each step of each iteration of the method.
		The display is color coded to show basic variables plus which variables are entering and leaving the basis.
	www-fp.mcs.anl.gov /otc/Guide/CaseStudies/simplex (154 words)

	Clustering for Faster Network Simplex Pivots - Eppstein (ResearchIndex)
		Abstract: We show how to use tree clustering techniques to improve the time bounds for optimal pivot selection in the primal network simplex algorithm for minimum cost flow, and for pivot execution in the dual network simplex algorithm for the same problem, from O(m)toO(# m) per pivot.
		Our techniques can also speed up network simplex algorithms for generalized flow, shortest paths with negative edges, maximum flow, the assignment problem, and the transshipment problem.
		6 Use of dynamic trees in a network simplex algorithm for the..
	citeseer.ist.psu.edu /eppstein93clustering.html (560 words)

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