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Topic: Nonlinear programming

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	Robert Burkhardt: Application of Nonlinear Programming to Tensegrity
		Nonlinear programming seems a good fit for the design of floating-compression tensegrity structures, since, as mentioned, the stability of these structures requires that certain extremal conditions be met.
		In general, when nonlinear programming is applied to design rather than validation, a weighted sum of second powers of member lengths appears in the objective function instead of the second power of the length of a single member.
		The nonlinear programming method described in Section 3 for designing skew prisms has been tested in designing skew N-prisms for N = 5, 6 and 8 with qualitative results identical to those described here for N = 3 and 4.
	members.tripod.com /bobwb/skew/skew.xml (5455 words)

	OR/MS Today - June 1998 - Software Survey
		Nonlinear programming is the "all of the above" of optimization models.
		That is, the nonlinear functions are approximated by linear functions, the solution of the linearized equations is used to get a new estimate of the optimum, and the whole process is repeated.
		Nonlinear programming includes such a broad range of models that warnings are to be expected.
	www.lionhrtpub.com /orms/orms-6-98/nlpss.html (2556 words)

	Preface: Nonlinear Programming
		Nonlinear programming is a mature field that has experienced major developments in the last ten years.
		There is a very extensive literature on nonlinear programming and to give a complete bibliography and a historical account of the research that led to the present form of the subject would have been impossible.
		One of the aims of the revision was to highlight the connections of nonlinear programming with other branches of optimization, such as linear programming, network optimization, and discrete/integer optimization.
	www.athenasc.com /nonlinpreface.html (1646 words)

	Nonlinear Programming FAQ
		Communicating with a nonlinear programming code can be particularly tedious and error-prone, especially if you have to write programs in a language like Fortran or C to compute function (and maybe gradient) values for your objective and constraints.
		Schittkowski, by Hock and Schittkowski, and by Torn and Zilinskas.
		Nonlinear problems are accepted in the form of a C or Fortran program or in modeling languages such as AMPL and GAMS.
	mccammon.ucsd.edu /~adcock/nonlinear-programming-faq.html (5752 words)

	Solver Technology - Smooth Nonlinear Optimization (Site not responding. Last check: 2007-11-01)
		It is also highly effective at solving linear programming (LP) and quadratic programming (QP) problems, and it handles problems of unlimited size, subject to available time and memory.
		The objective of this QP subproblem is a quadratic approximation of a modified Lagrangian function that depends on the nonlinear problem's objective and constraints; the constraints of the QP subproblem are linearizations at the current point of the nonlinear problem's constraints.
		It uses "elastic programming" techniques to deal with infeasibility in the original problem and the QP subproblems; for infeasible models, it is more likely to arrive at a "close to feasible" solution than most other SQP solvers.
	www.solver.com /technology4.htm (883 words)

	Nonlinear programming - Wikipedia, the free encyclopedia
		In mathematics, nonlinear programming (NLP) is the process of solving a system of equalities and inequalities over a set of unknown real variables, along with an objective function to be maximized or minimized.
		If the objective function f is linear and the constrained space is a polytope, the problem is a linear programming problem, which may be solved using well known linear programming solutions.
		Another method involves the use of branch and bound techniques, where the program is divided into subclasses to be solved with linear approximations that form a lower bound on the overall cost within the subdivision.
	en.wikipedia.org /wiki/Nonlinear_programming (384 words)

	Nonlinear Programming FAQ
		Luenberger, Introduction to Linear and Nonlinear Programming, Addison Wesley, 1984.
		Nonlinear problems in the form of a C or Fortran program may be submitted by sending e-mail, by submitting URLs through a Web page, or via a high-speed socket-based Unix interface.
		Nonlinear programs in the AMPL modeling language can also be sent to some of the solvers using
	frcatel.fri.utc.sk /nonlinear-programming-faq.html (4968 words)

	Linear and Nonlinear Programming (Site not responding. Last check: 2007-11-01)
		(The term "programming" dates from the 1940s and the discipline of "planning and programming" where these solution methods were first used; it has nothing to do with computer programming.) If the problem includes integer constraints, it is called an integer linear or integer nonlinear programming problem, respectively.
		A linear programming problem with some "regular" (continuous) decision variables, and some variables which are constrained to integer values, is called a mixed-integer programming (MIP) problem.
		A quadratic programming (QP) problem can be thought of as a generalization of a linear programming problem, or as a restricted case of a nonlinear problem.
	www.frontsys.com /123/lts00020.htm (245 words)

	TMT602: Nonlinear programming (Site not responding. Last check: 2007-11-01)
		Although nonlinear programming problems are generally difficult to solve in practice, effective algorithms for solving particular cases such as linear or convex programming now exist, and understanding the theory of nonlinear programming aften allows one to formulate his problem that can be solved efficiently.
		The goal of this course is to help the student develop a working knowledge of nonlinear programming, in particular convex optimization, i.e., to develop the skills and background needed to formulate, analyze and solve nonlinear problems.
		The course Nonlinear programming at the MIT by Professor Dimitri Bertsekas
	cg.ensmp.fr /~vert/teaching/2006insead/index.html (727 words)

	90: Operations research, mathematical programming
		90C (Mathematical programming) is one of the largest 3-digit areas (and 90C30 (nonlinear programming) is one of the largest 5-digit areas!), but the other subfields were also fairly large.
		Starting in the year 2000 sections A and D were removed from this heading; a new primary classification Game theory, economics, social and behavioral sciences will be added which will include most of what has been in those sections.
		Using linear programming to answer questions with binary variables (an example of a transportation problem).
	www.math.niu.edu /~rusin/known-math/index/90-XX.html (545 words)

	Nonlinear goal programming using multi-objective genetic algorithms
		Goal programming is a technique often used in engineering design activities primarily to find a compromised solution which will simultaneously satisfy a number of design goals.
		Third, since most real-world goal programming problems involve nonlinear criterion functions, the resulting single-objective optimization problem becomes a nonlinear programming problem, which is difficult to solve using classical optimization methods.
		In tackling nonlinear goal programming problems, although successive linearization techniques have been suggested, they are found to be sensitive to the chosen starting solution.
	www.palgrave-journals.com /jors/journal/v52/n3/abs/2601089a.html (342 words)

	Nonlinear Programming FAQ
		A further special case of great importance is where the objective function is entirely linear; this is called Linear Programming (LP) and is discussed in a separate FAQ list.
		For nonlinear optimization problems with both continuous and binary variables (MINLP), there is a code called DICOPT++, available commercially from GAMS Development Corp. Contact gams@gams.com for more information.
		The following are a few of the codes available in this area: * BARON consists of a "core" module for global nonlinear optimization in continuous and/or discrete variables, and a variety of specialized modules for such problems as bilinear programming, fixed-charge programming, indefinite quadratic programming, linear multiplicative programming, and univariate polynomial programming.
	www.faqs.org /faqs/nonlinear-programming-faq (4771 words)

	Nonlinear Programming FAQ
		DFO, a package for solving small-scale nonlinear problems typical of engineering design, where the objective is relatively expensive to compute and derivatives are not available.
		LEVMAR is an implementation of the Levenberg-Marquardt algorithm for nonlinear least squares problems, written by Manolis Lourakis.
		Offers access to several dozen solvers for linear and nonlinear programming, network and stochastic linear programming, unconstrained and bound-constrained optimization of nonlinear functions, and nonlinear complementarity.
	www-unix.mcs.anl.gov /otc/Guide/faq/nonlinear-programming-faq.html (5846 words)

	The Math Forum - Math Library - Nonlinear Progrmng (Site not responding. Last check: 2007-11-01)
		A Mathematica package that provides a suite of tools for solving nonlinear optimization problems, as well as a variety of other applications such as finding the roots or zeros of a non-analytic function.
		Nonlinear optimization is a course that offers a blend of heuristics and rigor, theory and experiment.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /library/topics/nonlinear_prog (858 words)

	Publications of Klaus Schittkowski (Site not responding. Last check: 2007-11-01)
		Abstract: Nonlinear programming is a direct extension of linear programming, when we replace linear model functions by nonlinear ones.
		However, to understand how optimization methods work, how corresponding programs are organized, how the results are to be interpreted, and, last not least, what are the limitations of the powerful mathematical technology, it is necessary to understand at least the basic terminology.
		The most popular classes of constrained nonlinear programming algorithms are introduced, i.e., penalty-barrier, interior point, augmented Lagrangian, sequential quadratic programming, sequential linear programming, generalized reduced gradient, and sequential convex programming methods.
	www.uni-bayreuth.de /departments/math/~kschittkowski/eolss.htm (179 words)

	[No title]
		These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions.
		Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming.
		Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints.
	www.ec-securehost.com /SIAM/CL10.html (332 words)

	Linear Programming FAQ
		Hence the phrase "LP program" to refer to a piece of software is not a redundancy, although I tend to use the term "code" instead of "program" to avoid the possible ambiguity.
		These methods derive from techniques for nonlinear programming that were developed and popularized in the 1960s by Fiacco and McCormick, but their application to linear programming dates back only to Karmarkar's innovative analysis in 1984.
		The network linear programming problem is to minimize the (linear) total cost of flows along all arcs of a network, subject to conservation of flow at each node, and upper and/or lower bounds on the flow along each arc.
	www-unix.mcs.anl.gov /otc/Guide/faq/linear-programming-faq.html (13600 words)

	Nonlinear Programming -- from Mathematica Information Center
		My own objective was to introduce students to the beauty of programming the methods only sketched in the text, to indicate what must be done to make algorithms that are practical, discuss some tradeoffs between various methods, and so on.
		This is an introductory graduate-student course in nonlinear programming.
		The focus is on theory and algorithmic methods for solving equations and for the related task of local optimization.
	library.wolfram.com /infocenter/Courseware/268 (249 words)

	Nonlinear Programming Packages
		APPSPACK is serial or parallel, derivative-free optimization software for solving nonlinear unconstrained, bound-constrained, and linearly-constrained optimization problems, with possibly noisy and expensive objective functions.
		Dense linear and quadratic programs (convex), and constrained linear least-squares problems.
		* nonlinear programming: PENNLP for general (smooth) large-scale nonlinear optimization and one of the fastest codes for (smooth) convex optimization.
	www.ici.ro /camo/hnp.htm (126 words)

	WORMS Brian's Digest: Nonlinear Programming
		Nonlinear Programming, by D. Bertsekas (Athena Publ.) 1995.
		The methods described there are implemented in a program I've written in Gauss called CML (a commerical product available from Aptech Systems).
		I'm just beggining to use a fl box nonlinear optimization routine (it comes with the language I'm currently using, IDL, and allows for bound constraints on the parameters as well as nonlinear constraint functions, both of which I need).
	www.worms.ms.unimelb.edu.au /digest/nlp.html (3327 words)

	CDC2000 Dynamic and Nonlinear Programming (Site not responding. Last check: 2007-11-01)
		In this paper, we present improved versions of the standard semidefinite relaxation for quadratic programming, that underlies many important results in robustness analysis and combinatorial optimization.
		In this paper, the value function for an optimal control problem with endpoint and state constraints is characterized as the unique lower semicontinuous generalized solution of the Hamilton-Jacobi Equation.
		In this paper, we present a hierarchy of semidefinite programming based sufficient conditions for a real matrix to be copositive.
	www.mm.anadolu.edu.tr /ieeecss/39cdc/CD00S185.HTM (609 words)

	Control Applications of Nonlinear Convex Programming
		In the last few years researchers have begun to appreciate a very important property of these interior-point methods (beyond their efficiency for LP): they extend gracefully to nonlinear convex optimization problems.
		New interior-point algorithms for problem classes such as semidefinite programming (SDP) or second-order cone programming (SOCP) are now approaching the extreme efficiency of modern linear programming codes.
		In this paper we discuss three examples of areas of control where our ability to efficiently solve nonlinear convex optimization problems opens up new applications.
	www.stanford.edu /~boyd/cvx-control.html (195 words)

	Downloads
		In the latter case, copy one of the self-extracting files into a temporary directory, execute the code, and save all files in an empty installation directory of your choice.
		Interactive user interface running under MS-Windows, to facilitate the formulation of nonlinear programming models, their implementation and numerical solution.
		It is possible to solve general nonlinear programming, least squares, L1, min-max and multicriteria problems interactively.
	www.uni-bayreuth.de /departments/math/~kschittkowski/downloads.htm (783 words)

	CAAM 664 - Topics in Nonlinear Programming
		This is the official webpage for "CAAM 664 - Topics in Nonlinear Programming".
		This semester we will deal with structured convex programming problems in a conic setting, and interior point methods to solving such problems.
		Yin Zhang will be giving two lectures on primal-dual interior point methods for SDP on the 13th, and 15th of November 2002.
	www4.ncsu.edu /~kksivara/caam664 (499 words)

	IOE 611 Nonlinear Programming (Site not responding. Last check: 2007-11-01)
		Prerequisites: A course in linear programming, equivalent to IOE 510.
		Course objectives: To expose the student to nonlinear models, their applications, how to construct them, and to algorithms for solving them satisfactorily
		Newton's method and simplicial methods for nonlinear equations.
	www-personal.umich.edu /~murty/611/index.html (114 words)

	Nonlinear Programming FAQ FAQ
		[ ] [ ] Nonlinear Programming Frequently Asked Questions Optimization Technology Center of Northwestern University and Argonne National Laboratory [ ] Posted monthly to Usenet newsgroup sci.op-research World Wide Web version: http://www.mcs.anl.gov/home/otc/Guide/faq/nonlinear-programming-faq.html Plain-text version: ftp://rtfm.mit.edu/pub/usenet/sci.answers/nonlinear-programming-faq Date of this version: August 1, 1997 * Q1.
		The code can be called from FORTRAN and applies to general nonlinear and mixed integer nonlinear programs.
		In addition, specialized modules are provided for several structured nonconvex problems including polynomial, fractional, multiplicative, quadratic and concave minimization problems.
	www.non.com /news.answers/nonlinear-programming-faq.html (4797 words)

	Nonlinear Programming Research
		My interest in nonlinear programming algorithms grew out of my research in transportation analysis.
		A common thread in my research endeavours is a wish to not only contribute to scientific knowledge, but also (and a wish that is equally strong) to place the existing knowledge in a unified framework; this is, in my view, a far too overlooked part of scientific research.
		The latest addition (2005) is a report on a core problem, namely one that often is referred to as the (continuous) nonlinear knapsack problem.
	www.math.chalmers.se /~mipat/nlp.html (1160 words)

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