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Topic: Optimization problems

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	IMA Thematic Year on Optimization, September 2002 - June 2003
		Problems arising in supply chain and logistics optimization are being studied in departments of operations research and management science, as well as by mathematicians and computer scientists.
		Recently several new optimization paradigms and approaches have been proposed which not only have generated a large body of extremely important algorithmic research but have also given birth to new and widely diverse areas to which mathematical optimization is now being and can be applied.
		Exposing the types of problems and simulation outputs of interest to industry to the developers of optimization algorithms and introducing derivative free optimization algorithms that have already been developed to those who wish to optimize some simulation model should have a major impact on this area.
	www.ima.umn.edu /optimization (2786 words)

	Max-Min
		We then provide a collection of statements of optimization problems together with visual demos that can be used within a lecture or assigned for students to use for practice.
		Optimization problems often involve a situation in which you are asked to determine a largest or smallest value.
		For this optimization problem it is easy to choose data that yields an optimal time that appears at an end point of the curve for which as sample is displayed.
	astro.temple.edu /~dhill001/maxmin/maxmin.html (2895 words)

	Maximum/Minimum Problems
		PROBLEM 9 : You are standing at the edge of a slow-moving river which is one mile wide and wish to return to your campground on the opposite side of the river.
		PROBLEM 15 : Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in a sphere of radius 2.
		PROBLEM 19 : Find the point P = (x, 0) on the x-axis which minimizes the sum of the squares of the distances from P to (0, 0) and from P to (3, 2).
	math.ucdavis.edu /~kouba/CalcOneDIRECTORY/maxmindirectory/MaxMin.html (1278 words)

	OPTIMIZATION
		The OPTIMAL SOLUTION (or "solution to the optimization problem") is values of decision variables xl, x2,...xn that satisfy the constraints and for which the objective function attains a maximum (or a minimum, in a minimization problem).
		A special case is dynamic optimization problems where the decision variables are not real numbers or integers but functions of one or more independent variables -- functions of time or space coordinates, for example.
		Dynamic optimization problems are sometimes referred to as "optimal control problems." There exist special techniques to solve such problems; they often make use of DISCRETIZATION of the independent variables, for example dividing the time axis into a number of intervals and considering the solutions to be constant over those intervals.
	pespmc1.vub.ac.be /ASC/OPTIMIZATIO.html (385 words)

	Nonlinear Programming FAQ (Site not responding. Last check: 2007-10-14)
		Global Optimization is a collection of functions for global nonlinear optimization that uses the Mathematica system as an interface for defining the nonlinear system to be solved and for computing function numeric values.
		Omuses/HQP comprises a solver for nonlinearly constrained large-scale optimization problems (especially with regular sparsity structure) and a front end based on C++ and ADOL-C. It uses a Newton-type SQP method, with an interior-point procedure for the treatment of constraints.
		Schittkowski, by Hock and Schittkowski, and by Torn and Zilinskas.
	www-unix.mcs.anl.gov /otc/Guide/faq/nonlinear-programming-faq.html (5821 words)

	Linear Optimization
		The problem may be one of reducing the cost of operation while maintaining an acceptable level of service, and profit of current operations, or providing a higher level of service without increasing cost, maintaining a profitable operation while meeting imposed government regulations, or "improving" one aspect of product quality without reducing quality in another.
		Optimization problems are often classified as linear or nonlinear, depending on whether the relationship in the problem is linear with respect to the variables.
		Optimization problems are classified according to the mathematical characteristics of the objective function, the constraints, and the controllable decision variables.
	home.ubalt.edu /ntsbarsh/opre640a/partVIII.htm (14154 words)

	Mathtools.net : MATLAB/Optimization
		Optimization is an important and expanding area that helps engineers and scientists find improved solutions to their problems.
		YALMIP is a MATLAB toolbox for rapid prototyping of optimization problems.
		CONDOR is a new optimizer whose aim is to find the minimum x* of an objective function F(x) (x is a vector whose dimension is between 1 and 150) using the least number of function evaluations of F(x).
	www.mathtools.net /MATLAB/Optimization (1485 words)

	Qrhetoric Calculus - Optimization
		In general, the optimization problems you will encounter here are something like you are given a certain amount of material, and you want to create the dimensions that will give it the biggest volume.
		It is possible to solve a problem without sticking precisely to the outline, but if you train with this outline, you will be able to use it unfailingly in problems that are otherwise impossible.
		In this problem, the width is equal to the length, because I said it had a square base.
	calculus.freehomepage.com /cal08.htm (1328 words)

	OhioLINK ETD: Lee, Kuo-chun
		Optimization problems are generally classified as two types of problems: constraint-satisfied problems and minimization problems.
		The demonstrated applications for the constraint-satisfied problems are: (1) four-coloring problems; (2) sorting problems; (3) knight's tour problems and others.
		Several demonstrated applications for the minimization problems are as follows: (1) max cut problems; (2) module orientation problems; (3) maximum clique problems.
	rave.ohiolink.edu /etdc/view?acc_num=case1055943354 (150 words)

	String Noninclusion Optimization Problems
		For every string inclusion relation there are two optimization problems: find a longest string included in every string of a given finite language, and find a shortest string including every string of a given finite language.
		As an example, the two well-known pairs of problems, the longest common substring (or subsequence) problem and the shortest common superstring (or supersequence) problem, are interpretations of these two problems.
		We also discuss restricted versions of the problems, correlations between the string inclusion and noninclusion problems, and generalized problems which are the string inclusion problems for one language and the string noninclusion problems for another.
	epubs.siam.org /sam-bin/dbq/article/23427 (340 words)

	Optimization problems (Site not responding. Last check: 2007-10-14)
		C 1,1 vector optimization problems and Riemann derivatives...
		Course on Metaheuristics for Combinatorial Optimization Problems in Operations R...
		Solving standard quadratic optimization problems via linear, semidefinite and co...
	www.scienceoxygen.com /math/179.html (218 words)

	7.4 Optimization Problems
		Optimization problems are be constructed by calling the following function.
		The following attributes and methods are useful for examining and modifying optimization problems.
		This function converts the optimization problem to a linear program in matrix form and then solves it using the solver described in section 6.1.
	www.ee.ucla.edu /~vandenbe/cvxopt/doc/s-lp.html (479 words)

	Neural Network Algorithms for Hypergraph Optimization Problems (Site not responding. Last check: 2007-10-14)
		Such problems are important from theoretical and practical point of view as there are many applications of hypergraph optimization problems in real world.
		For a given set of templates the problem is to assign elements to the minimum number of memory modules in such a way that for each template all its elements are stored in different memory modules.
		The objective remains to optimize a problem on the primal variables; the target variables are employed to assist this process.
	www.msci.memphis.edu /~kaznad/Overview.html (3269 words)

	Calculus I (Math 2413) - Applications of Derivatives - Optimization
		In this section we are going to look at another type of optimization problem. Here we will be looking for the largest of smallest values of a function subject to some kind of constraint. It’s usually easiest to see how these work with some examples.
		In all of these problems we will have two functions. The first is the function that we are actually trying to optimize and the second will be some constraint. The constraint will be an equation that must be true no matter what else is happening in the problem.
		In this problem we want to maximize the area of a field and we know that will use 500 ft of fencing material. So, the area will be the function we are trying to optimize and the amount of fencing is the constraint.
	tutorial.math.lamar.edu /AllBrowsers/2413/Optimization.asp (1718 words)

	Monotonic Optimization: Problems and Solution Approaches
		Problems of maximizing or minimizing monotonic functions of n variables under monotonic constraints are discussed.
		A general framework for monotonic optimization is presented in which a key role is given to a property analogous to the separation property of convex sets.
		The approach is applicable to a wide class of optimization problems, including optimization problems dealing with functions representable as differences of increasing functions (d.i.
	epubs.siam.org /sam-bin/dbq/article/35982 (133 words)

	optimization problem (Site not responding. Last check: 2007-10-14)
		See also decision problem, optimal solution, optimal value, geometric optimization problem, witness, local optimum, global optimum, Classical optimization problems: bin packing problem, knapsack problem, cutting stock problem, Chinese postman problem, traveling salesman, vehicle routing problem, prisoner's dilemma, Solution methods: dynamic programming, metaheuristic, relaxation, simulated annealing.
		For instance, the traveling salesman problem is an optimization problem, while the corresponding decision problem asks if there is a Hamiltonian cycle with a cost less than some fixed amount k.
		AUTHOR(S), "optimization problem", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/optimization.html (234 words)

	Ancient Greek Optimization Problems
		Pappus introduces this problem with one of the most charming essays in the history of mathematics, one that has frequently been excerpted under the title On the Sagacity of Bees.
		Pappus speaks poetically of the divine mission of the bees to bring from heaven the wonderful nectar known as honey, and says that in keeping with this mission they must make their honeycombs without any cracks through which honey could be lost.
		Inasmuch as Pappus showed that of two regular polygons having equal perimeters the one with the greater number of sides has the greater area, he concluded that bees demonstrated some degree of mathematical understanding in constructing their cells as hexagonal, rather than square or triangular prisms.
	www.mlahanas.de /Greeks/Optimization.htm (2077 words)

	Course on Metaheuristics for Combinatorial Optimization Problems in Operations Research (Site not responding. Last check: 2007-10-14)
		We encountered this problem while studying a learning model in which we seek the minimum sized set of training examples needed to teach a given geometric concept to a nearest neighbor learning program.
		Another good starting point for those interested in NP-Hard optimization problems and in particular in some Operations Research problems involving routing is Bernard Moret's list of publications since many of them are available in postscript form.
		We are interested in the combinatorial optimization aspects of folding a simple chain of hydrophobic-hydrophilic elements on a square lattice.
	www.ing.unlp.edu.ar /cetad/mos/geometric.html (1597 words)

	ILOG CPLEX: High-performance software for mathematical programming and optimization
		ILOG pioneered development of the algorithms needed to solve today's most demanding mathematical optimization problems.
		ILOG CPLEX has solved problems with millions of constraints and variables, and consistently sets new standards for mathematical programming software performance.
		ILOG CPLEX optimizers deliver the power needed to solve very large, real-world optimization problems, as well as the speed required by today's interactive applications.
	www.ilog.com /products/cplex (397 words)

	NEOS Guide: Optimization Software
		FSQP - nonlinear and minmax constrained optimization, with feasible iterates.
		OPL Studio - optimization language and solver environment.
		PROC NLP - various quadratic and nonlinear optimization problems.
	www-fp.mcs.anl.gov /otc/Guide/SoftwareGuide (274 words)

	NEOS Server for Optimization (Site not responding. Last check: 2007-10-14)
		Optimization problems are solved automatically with minimal input from the user.
		Users only need a definition of the optimization problem; all additional information required by the optimization solver is determined automatically.
		To submit your optimization job, first click on the NEOS Solvers icon to find a suitable solver.
	www-neos.mcs.anl.gov /neos (242 words)

	Global Optimization (Site not responding. Last check: 2007-10-14)
		SIAM maintains a collection of Optimization Books and Proceeedings on local (and some global) optimization, and there are also some other Global Optimization Books.
		For general problems, you have to provide your own underestimation routines which may still be a lot of programming work.
		Many but not all of these problems have several local minima, but any reasonable global optimization algorithms should be able to cope with unique minimizers, too, without a huge overhead over local techniques.
	www-aig.jpl.nasa.gov /public/home/decoste/HTMLS/NN/glopt/glopt.html (1573 words)

	[Ga-list] Global Optimization Test Problems.htm (Site not responding. Last check: 2007-10-14)
		Software 7 (1981), 17-41,=0A= =0A= optionally together with the bounds from=0A= =0A= Gay, D.M., A trust-region approach to linearly constrained=0A= optimization, pp.
		=0A= =0A= The =0A= =0A= Morandeacute;/Garbow/Hillstrom test problems =0A= are standard test problems for the case of continuous variables when =0A= only one solution is requested.
		It was designed for testing (low-dimensional) local=0A= optimization algorithms, but most of these test problems are nonconvex =0A= and possess several local minima with different objective function =0A= values.
	www.cse.msu.edu /pipermail/ga-list/2001-November/000028.html (262 words)

	COPS: Large-Scale Optimization Problems (Site not responding. Last check: 2007-10-14)
		Problems in the current version of the collection come from fluid dynamics, population dynamics, optimal design, mesh smoothing, and optimal control.
		For each problem we provide a short description of the problem, notes on the formulation of the problem, and results of computational experiments with general optimization solvers.
		The COPS collection of problems can be obtained by entering your email address below (so that you can be informed of future software updates) and downloading the compressed tar file that contains the AMPL model and data files (Version 3.0) or the compressed tar file of GAMS models (Version 2.0).
	www-unix.mcs.anl.gov /~more/cops (264 words)

	Solving Optimization Problems with AMPL and NEOS
		In the conventional approach to solving optimization problems, the user must first identify and obtain the appropriate piece of optimization software; write code to define the problem in the manner required; and then compile, link, and run the software.
		Given the definition of a nonlinear optimization problem, NEOS determines an appropriate solver, uses automatic differentiation tools to compute derivatives and sparsity patterns, compiles all subroutines, links with the appropriate libraries, and executes the solver.
		AMPL is a comprehensive and powerful modeling language for optimization problems that simplifies the formulation of optimization problems.
	www.crpc.rice.edu /newsletters/win98/wip_neos.html (454 words)

	Parallel Algorithms for Global Optimization Problems (ResearchIndex)
		Abstract: In this chapter we discuss parallel algorithms for solving some classes of global optimization problems.
		We present an introductory survey of parallel algorithms that have been used to solve structured problems (partially separable, and large-scale block structured problems), algorithms based on parallel local searches, Monte Carlo approaches and parallel algorithms for some location problems.
		Parallel Approximation of Optimization Problems (Extended abstract) - al.
	citeseer.ist.psu.edu /185017.html (504 words)

	Benchmarks for Optimization Software
		The number of optimization solvers we are making available for use through NEOS has also been reduced.
		Several SDP codes on problems from SDPLIB (6-23-2005)
		SQL problems from the 7th DIMACS Challenge (8-8-2002)
	plato.la.asu.edu /bench.html (150 words)

	Handbook of Test Problems for Local and Global Optimization
		This web site is intended to be a supplement to the Handbook of Test Problems in Local and Global Optimization published by Kluwer Academic Publishers.
		The principal objective of this book is to present a collection of challenging test problems arising in literature studies and a wide spectrum of applications.
		The algebraic test problems are available in the GAMS modeling language and the differential-algebraic problems are supplied in the MINOPT modeling language.
	titan.princeton.edu /TestProblems (265 words)

	A compendium of NP optimization problems
		Graph Theory: Vertex Ordering, Network Design: Cuts and Connectivity.
		This is a continuously updated catalog of approximability results for NP optimization problems.
		The compendium is also a part of the book
	www.nada.kth.se /~viggo/problemlist/compendium.html (82 words)

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