
	Where results make sense

Topic: Convex programming

	Convex Web Programming \| Website Design \| Web Site Company
		Convex optimization is a subfield of mathematical optimization.
		A twice differentiable function of one variable is convex on an interval if and only if its second derivative is non-negative there; this gives a practical test for convexity.
		More generally, a continuous, twice differentiable function of several variables is convex on a convex set if and only if its Hessian matrix is positive semidefinite on the interior of the convex set.
	www.atozsolution.com /convex_web_programming (194 words)

	A decomposition method for quadratic programming. (Technical) - HighBeam Encyclopedia (Site not responding. Last check: 2007-10-17)
		The quadratic programs have linear constraints, the variables are subject to nonnegativity constraints, and the objective function has a linear and a quadratic part where the quadratic part is convex.
		One property of quadratic programs that makes them potentially more difficult to slve than linear programs with the same number of variables and constraints is that, unlike the solution to a linear program, the solution to a quadratic program may necessarily use all the variables of the problem.
		In the case of quadratic programming, scaling applied to the constraint matrix must also be applied to the quadratic part of the objective function Q. Since Q A may be out of scale with respect to each other, this technique may not be as effective.
	www.encyclopedia.com /doc/1G1-11936986.html (4307 words)

	Mohit Tawarmalani's Publications
		We define a convex extension of a lower-semicontinuous function to be a convex function that is identical to the given function over a pre-specified subset of its domain.
		Finally, using the theory of convex extensions we characterize the precise gaps exhibited by various underestimators of x/y over a rectangle and prove that the extensions theory provides convex relaxations that are much tighter than the relaxation provided by the classical outer-linearization of bilinear terms.
		Finally, we derive the convex envelope for a class of functions of the type f(x,y) over a hypercube under the assumption that f is concave in x and convex in y.
	archimedes.scs.uiuc.edu /tawarmal/research.html (1130 words)

	[No title]
		Convex Analysis and Optimization, Lecture Slides for MIT course 6.253.
		In particular, we embed the problem within a dynamic programming framework, and we introduce several types of rollout algorithms, which are related to notions of policy iteration.
		We have developed distributed iterative algorithms for solving a more general version of this integer programming problem, which is of independent interest, and have shown that they find the optimal solution in a finite number of iterations which is polynomial in the number of power levels and the number of mobiles.
	web.mit.edu /dimitrib/www/publ.html (13742 words)

	Preface: Network Flows and Monotropic Optimization
		In both network programming and linear programming, conditions for feasibility or optimality typically concern the relationships between a primal problem and a dual problem, and these relationships have a deep practical significance.
		One is not so much involved with constraint functions and their associated Lagrange multipliers, which are the prime focus in convex and nonconvex programming more generally, as one is with pairs of primal and dual variables whose values must fall into a certain pattern with respect to each other.
		Among the by-products of this are extensions of the simplex method of linear programming and the out-of-kilter algorithm of network programming to general piecewise linear programming and beyond.
	www.athenasc.com /rockpreface.html (1558 words)

	MS67 Interior-Point Methods and Convex Programming (Part I of II)
		Interior-Point Methods and Convex Programming (Part I of II)
		Much of the success for the linear case has followed through to the convex programming case, e.g.
		Although the success for interior-point methods has not yet followed through to the general nonlinear programming case, there are many promising steps in this direction.
	www.siam.org /meetings/an98/ms67.htm (251 words)

	Amazon.ca: Separable Programming : Theory and Methods: Books: S.M. Stefanov (Site not responding. Last check: 2007-10-17)
		In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming.
		Some general results are presented, techniques of approximating the separable problem by linear programming and dynamic programming are considered.
		Convex separable programs subject to inequality/ equality constraint(s) and bounds on variables are also studied and iterative algorithms of polynomial complexity are proposed.
	www.amazon.ca /Separable-Programming-Methods-S-M-Stefanov/dp/0792368827 (350 words)

	Publications (in mathematics) list for Henry Wolkowicz
		A semidefinite programming, SDP, relaxation for the graph partitioning problem, GP, is derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of GP.
		Semidefinite programming (SDP) relaxations for the quadratic assignment problem (QAP) are derived using the dual of the (homogenized) Lagrangian dual of appropriate equivalent representations of QAP.
		Semidefinite linear programming (SDP) is a generalization of LP where the nonnegativity constraints are replaced by a semidefiniteness constraint on the matrix variables.
	orion.math.uwaterloo.ca /~hwolkowi/henry/reports/ABSTRACTS.html (11292 words)

	Applied Mathematics: Faculty (Site not responding. Last check: 2007-10-17)
		"Monotropic programming: a generalization of linear programming and network programming," in Convexity and Duality in Optimization, J. Ponstein (ed.), Springer-Verlag Lecture Notes in Economics and Math.
		Programming, H. Kuhn and A. Tucker (eds.), Dept. of Math., Princeton University, 1970, 418-485.
		"A monotone convex analog of linear algebra," in Proc.
	www.amath.washington.edu /people/faculty/rockafellar/publications.html (2505 words)

	ISMP 2000 - Meeting Topics (Site not responding. Last check: 2007-10-17)
		Consider minimization problems with convex separable objective function subject to a separableconvex inequality constraint of the form "less than or equal to" /linear equality constraint /linear inequality constraint of the form "greater than or equal to", and bounds on the variables.
		It is considered an implicit iterative method in linear programming, which combines an inexact version of the proximal point algorithm with the standard one-parameter exponential penalty.
		It is shown that the generated primal sequence converges towards an optimal solution of the linear program.
	www.isye.gatech.edu /ismp2000/schedule/session_pages/WEA-08-IC117.html (310 words)

	[No title]
		Fischer A Newton-type method for sparse quadratic programming problems SESSION 3: Convex Programming - A. Auslender (TA21) K.D. Andersen A Newton barrier method for minimizing a sum of norms subject to linear equality constraints and an efficient method to handle the L1 penalty function W.
		Monteiro On the existence and convergence of the central path for convex programming V.
		Venets Continuous optimization algorithms and their finite convergence in convex cases SESSION 6: Convex Programming - R. Mifflin (TF21) W.T. Obuchowska Minimal representation of convex regions D.L. Jensen The convergence of a modified barrier method for convex programming R.
	www.informs.org /conf/Arbor/Program/Sess2 (13309 words)

	Mathematical Programming. (Site not responding. Last check: 2007-10-17)
		D.S. Atkinson, P.M. Vaidya, A cutting plane algorithm for convex programming that uses analytic centers, Mathematical Programming 69 (1) (1995) pp.
		M.A. Nunez, R.M. Freund, Condition measures and properties of the central trajectory of a linear program, Mathematical Programming 83 (1) (1998) pp.
		Frauendorfer, Barycentric scenario trees in convex multistage stochastic programming, Mathematical Programming 75 (2) (1996) pp.
	www.elsevier.com /cdweb/journals/00255610/viewer.htt?viewtype=keywords&rangeselected=2 (713 words)

	The convergence of a modified barrier method for convex programming
		We show, using elementary considerations, that a modified barrier function method for the solution of convex programming problems converges for any fixed positive setting of the barrier parameter.
		With mild conditions on the primal and dual feasible regions, we show how to use the modified barrier function method to obtain primal and dual optimal solutions, even in the presence of degeneracy.
		We illustrate the argument for convergence in the case of linear programming, and then generalize it to the convex programming case.
	www.research.ibm.com /journal/rd/383/jensen.html (102 words)

	Research - Prof. Carlton Scott, GSM, UCI
		A new theory for quasi-concave programming and equilibrium problems which has particular relevance to economics (29, 38, 39, 40).
		Currently I am writing a book entitled, "Convex Programming: Analysis and Application," with T. Jefferson, which will highlight the role of prior analysis in facilitating the solution of optimization problems.
		"Duality for Convex and Nonconvex Sum of Ratios," Mathematical Programming Conference, Lausanne, 1997.
	www.gsm.uci.edu /~SCOTT/research.htm (2290 words)

	erasmus mundus
		This course introduces the student to the mathematical foundations of convexity and optimization and their use in economic models.
		Convex and concave functions, graph, epigraph and hypograph.
		Proof of the Kuhn-Tucker theorem in convex programming.
	www.univ-paris1.fr /formation/eco_gestion/ufr27/study-in-english/erasmus_mundus/intranet/courses/article5496.html (186 words)

	Optimization Online - A New Self-Dual Embedding Method for Convex Programming
		Abstract: In this paper we introduce a conic optimization formulation for inequality-constrained convex programming, and propose a self-dual embedding model for solving the resulting conic optimization problem.
		The primal and dual cones in this formulation are characterized by the original constraint functions and their corresponding conjugate functions respectively.
		For this purpose, as one application, we prove that the barrier functions constructed this way are indeed self-concordant when the original constraint functions are convex and quadratic.
	www.optimization-online.org /DB_HTML/2002/01/423.html (229 words)

	Citations: analytic center' for polyhedrons and new classes of global algorithms for linear (smooth, convex) ...
		Sonnevend, G. An analytic center for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming.
		Sonnevend, "An 'analytic center' for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming," Proc.
		Sonnevend, "An `analytic center' for polyhedrons and new classes of global algorithms for linear (smooth, convex) programming," Institute of Mathematics, Etvos University, Hungary, 1985.
	citeseer.ist.psu.edu /context/62113/0 (1128 words)

	Amazon.ca: Modified Lagrangians and Monotone Maps in Optimization: Books: E. G. Golshtein,N. V. Tretyakov (Site not responding. Last check: 2007-10-17)
		Providing a thorough analysis for both traditional convex programming and monotone maps, the book shows the advantages of MLFs over classical Lagrangian functions in such practical applications as numerical algorithms, economic modeling, de-composition, and nonconvex local constrained optimization.
		Focusing on two key areas, traditional convex programming and monotone maps, the book explores a number of practical applications for MLFs and shows how MLFs are especially relevant to traditional convex programming.
		Covers convex programming methods that are based on the iterative solution of dual problems generated by MLFs, showing how the proper choice of an MLF can guarantee the smoothness of the results
	www.amazon.ca /Modified-Lagrangians-Monotone-Maps-Optimization/dp/0471548219 (781 words)

	Well It Was Twenty Years Ago Today... \| Open Source Initiative
		Early benchmarks showed it was as fast, and occasionally faster than the "big science" vector compiler when used on mostly scalar code.
		This made the compiler group manager even less happy, since he also had a two person group working on an 'advanced' debugger for the Convex machines that was far worse than GDB (and the X Window System interface to gdb just blew the doors off that project.)
		Subsequent to my leaving Convex, politics prevailed, and it became a fireable offense for the guys in "Technical Marketing" to use GCC in a customer benchmark.
	www.opensource.org /node/155 (1253 words)

	Convex Programming (Site not responding. Last check: 2007-10-17)
		For the convex programming problem, we used the non-linear program solver LOQO, which uses an infeasible primal-dual interior point approach to solve the program.
		The solver works better on convex programs than non-convex progams.
		We only measure the time taken by the solver and not the time taken in generating and preparing the input.
	www.cs.uiowa.edu /~rraman/eq/mkts/node10.html (67 words)

	An Interior Point Subgradient Method for Linearly Constrained Nondifferentiable Convex Programming (SMEALSearch) - ... (Site not responding. Last check: 2007-10-17)
		We propose in this paper an algorithm for solving linearly constrained nondifferentiable convex programming problems.
		6 A new polynomial-time algorithm for linear programming (context) - Karmarkar - 1984
		5 Interior-point polynomial algorithms in convex programming (context) - Nesterov, Nemirovskii - 1994
	smealsearch2.psu.edu /2587.html (518 words)

	DC MetaData for: Sequential convex programming methods (Site not responding. Last check: 2007-10-17)
		Sequential convex programming methods became very popular in the past for special domains of application, e.g.
		The algorithm uses an inverse approximation of certain variables so that a convex, separable nonlinear programming problem must be solved in each iteration.
		In this paper the method is outlined and it is shown, how the iteration process can be stabilized by a line search.
	www.uni-bayreuth.de /departments/math/~czillober/abstracts/marti.html (130 words)

	Hessian Riemannian Gradient Flows in Convex Programming
		The first result characterizes Hessian Riemannian structures on convex sets as metrics that have a specific integration property with respect to variational inequalities, giving a new motivation for the introduction of Bregman-type distances.
		Dual trajectories are identified, and sufficient conditions for dual convergence are examined for a convex program with positivity and equality constraints.
		In the case of a linear objective function, several optimality characterizations of the orbits are given: optimal path of viscosity methods, continuous-time model of Bregman-type proximal algorithms, geodesics for some adequate metrics, and projections of $\dot q$-trajectories of some Lagrange equations and completely integrable Hamiltonian systems.
	epubs.siam.org /sam-bin/dbq/article/41997 (235 words)

	Brian's Digest: Convex Programming
		Given the point oracle returns me whether it is inside or outside of convex and, if it is outside, normal vector of cutting plane.
		SDP is a generalization of linear programming to the space of block diagonal, symmetric, positive semidefinite matrices.
		where the objective function and the constraint functions are all convex and the feasible region is assumed to be a well-rounded subset of R^n.
	www.worms.ms.unimelb.edu.au /digest/convex_prog.html (1856 words)

	Interior Point Column Generation Algorithms for Convex Programming (Site not responding. Last check: 2007-10-17)
		MB07.2 Nonlinear Programming with Constraints Given by an Oracle Jean-Louis Goffin, Faranak Sharifi Mokhtarian --- McGill Univ., Fac.
		The nonlinear analytic center cutting plane method can be applied to the solution of problems with a smooth nonlinear objective and constraints given by a separation oracle.
		Consider a nonempty convex set defined by a finite number of convex differentiable inequalities admitting a self-concordant logarithmic barrier.
	www.informs.org /Conf/SD97/TALKS/MB07.html (253 words)

	An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming
		An Unconstrained Convex Programming Approach to Linear Semi-Infinite Programming: SIAM Journal on Optimization Vol.
		In this paper, an unconstrained convex programming dual approach for solving a class of linear semi-infinite programming problems is proposed.
		semi-infinite programming, linear programming, convex programming, entropy optimization
	epubs.siam.org /sam-bin/dbq/article/27621 (115 words)

	CVX -- Matlab Software for Disciplined Convex Programming
		Under this approach, convex functions and sets are built up from a small set of rules from convex analysis, starting from a base library of convex functions and sets.
		Geometric programs are not convex, but can be made so by applying a certain transformation.
		Between July 2005 and March 2006, a number of incremental improvements and bug fixes were made, culminating in the release of 0.93 alpha in March 2006.
	www.stanford.edu /~boyd/cvx (995 words)

Try your search on: Qwika (all wikis)