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Topic: Convex optimization

Related Topics

convex hull

convex function

Locally convex topological vector space

Convex Computer

locally convex

convex lens

Proper convex function

Minimal convex decomposition

convex set

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Plano convex

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	Convex Optimization
		Convex optimization problems are far more general than linear programming problems, but they share the desirable properties of LP problems: They can be solved quickly and reliably up to very large size -- hundreds of thousands of variables and constraints.
		A convex optimization problem is a problem where all of the constraints are convex functions, and the objective is a convex function if minimizing, or a concave function if maximizing.
		In a convex optimization problem, the feasible region -- the intersection of convex constraint functions -- is a convex region, as pictured below.
	www.solver.com /probconvex.htm (779 words)

	FreeTechBooks.com - Convex Optimization (Site not responding. Last check: 2007-10-22)
		This book is about convex optimization, a special class of mathematical optimization problems, which includes least-squares and linear programming problems.
		The book's main goal is to help the reader develop a working knowledge of convex optimization, i.e., to develop the skills and background needed to recognize, formulate, and solve convex optimization problems.
		The book's primary focus is on the latter group, the potential users of convex optimization, and not the (less numerous) experts in the field of convex optimization.
	www.freetechbooks.com /about370.html (523 words)

	EE227A Home Page (Site not responding. Last check: 2007-10-22)
		Convex optimization relates to a class of nonlinear optimization problems where the objective to be minimized, and the constraints, are both convex.
		Convex optimization problems are attractive because a large class of these problems can now be efficiently solved.
		Convex optimization is especially relevant when the data of the problem at hand is uncertain, and "robust" solutions are sought.
	www.eecs.berkeley.edu /~elghaoui/courses_files/ee227a/index.html (1200 words)

	Convex function - Wikipedia, the free encyclopedia
		A convex function f defined on some open interval C is continuous on C and differentiable at all but at most countably many points.
		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.
		However, a function whose level sets are convex sets may fail to be a convex function; such a function called a quasiconvex function.
	en.wikipedia.org /wiki/Convex_function (622 words)

	Convex optimization - Wikipedia, the free encyclopedia
		Convex optimization is a subfield of mathematical optimization.
		defined on a convex subset A of X, the problem is to find the point x in A for which the number f(x) is smallest.
		The convexity of A and f makes the powerful tools of convex analysis applicable: the Hahn-Banach theorem and the theory of subgradients lead to a particularly satisfying and complete theory of necessary and sufficient conditions for optimality, a duality theory comparable in perfection to that for linear programming, and effective computational methods.
	en.wikipedia.org /wiki/Convex_optimization (278 words)

	IFOR - Convex Optimization SS06 (Site not responding. Last check: 2007-10-22)
		Convexity plays a central role in the design and analysis of modern and highly successful algorithms for solving real-world optimization problems.
		The lecture (in English) on convex optimization will treat in a balanced manner theory (convex analysis, optimality conditions) and algorithms for convex optimization.
		Beginning with basic concepts and results about the structure of convex sets, continuity and differentiability of convex functions (including conjugate functions), the lecture will cover systems of inequalities, the minimum (or maximum) of a convex function over a convex set, Lagrange multipliers, duality theory and mini-max theorems.
	www.math.ethz.ch /ifor/teaching/previous/convexopt (494 words)

	Dattorro's Storefront - Lulu.com
		Optimization is the science of making a best choice in the face of conflicting requirements.
		If a given optimization problem can be transformed to a convex equivalent, then this interpretive benefit is acquired.
		This book is about convex optimization, convex geometry (with particular attention to distance geometry), geometrical problems, and problems that can be transformed into geometrical problems.
	www.lulu.com /dattorro (545 words)

	Optimization Online - Convex Approximations of Chance Constrained Programs
		Our goal is to build a computationally tractable approximation of this (typically intractable) problem, i.e., an explicitly given convex optimization program with the feasible set contained in the one of the chance constrained problem.
		Moreover, under the assumptions that the constraints are affine in the perturbations and the entries in the perturbation vector are independent of each other random variables, we build a large deviations type approximation, referred to as `Bernstein approximation', of the chance constrained problem.
		Finally, we extend our construction to the case of ambiguously chance constrained problems, where the random perturbations are independent with the collection of distributions known to belong to a given convex compact set rather than to be known exactly, while the chance constraint should be satisfied for every distribution given by this set.
	www.optimization-online.org /DB_HTML/2004/12/1033.html (256 words)

	Convex Optimization - Cambridge University Press (Site not responding. Last check: 2007-10-22)
		Convex optimization problems arise frequently in many different fields.
		The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems.
		The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521833787 (357 words)

	Optimization Problem Types - Overview
		In an optimization problem, the types of mathematical relationships between the objective and constraints and the decision variables determine how hard it is to solve, the solution methods or algorithms that can be used for optimization, and the confidence you can have that the solution is truly optimal.
		A key issue is whether the problem functions are convex or non-convex: Click Convex Optimization Problems to learn more.
		If the objective and all constraints are convex, you can be confident of determining whether there is a feasible solution, finding the globally optimal solution, and solving the problem up to very large size.
	www.solver.com /probtype.htm (424 words)

	CAAM 554: Convex Optimization, Fall 2006
		Scope: Convex optimization problems arise in communication, system theory, VLSI, CAD, finance, inventory, network optimization, learning, computer vision, statistics, etc. Thanks to the recent advances in interior-point methods, various new solvers are now available and have made solving convex problems ever easier.
		Nevertheless, problems are often unrecognized as convex and, therefore, remain unsolved.
		This course is designed to be an exposure to convex optimization problems, their solution techniques and applications.
	www.caam.rice.edu /~wy1/CAAM554 (235 words)

	Amazon.co.uk: Convex Optimization: Books: Stephen Boyd,Lieven Vandenberghe (Site not responding. Last check: 2007-10-22)
		Convex optimization problems arise frequently in many different fields.
		The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems.
		The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them.
	www.amazon.co.uk /Convex-Optimization-Stephen-Boyd/dp/0521833787 (512 words)

	ETH - Computer Science - Details (Site not responding. Last check: 2007-10-22)
		Convexity plays a central role in the design and analysis of modern and highly successful algorithms for solving real-world optimization problems.
		The lecture (in English) on convex optimization will treat in a balanced manner theory (convex analysis, optimality conditions) and algorithms for convex optimization.
		Beginning with basic concepts and results about the structure of convex sets, continuity and differentiability of convex functions (including conjugate functions), the lecture will cover systems of inequalities, the minimum (or maximum) of a convex function over a convex set, Lagrange multipliers, duality theory and mini-max theorems.
	www.inf.ethz.ch /education/courses/detail?id=401-3904-00 (260 words)

	Convex optimization problems involving finite autocorrelation sequences
		ABSTRACT: We discuss convex optimization problems where some of the variables are constrained to be finite autocorrelation sequences.
		Autocorrelation constraints in optimization problems are often approximated by sampling the corresponding power spectral density, which results in a set of linear inequalities.
		The linear matrix inequality formulation is exact, and results in convex optimization problems that can be solved using interior-point methods for semidefinite programming.
	www.ee.ucla.edu /~vandenbe/alv01b.htm (178 words)

	SSRN-Complexity of Convex Optimization Using Geometry-Based Measures and a Reference Point by Robert Freund
		Our concern lies in solving the following convex optimization problem: minimize cx subject to Ax=b, x \in P, where P is a closed convex set.
		We bound the complexity of computing an almost-optimal solution of this problem in terms of natural geometry-based measures of the feasible region and the level-set of almost-optimal solutions, relative to a given reference point x^r that might be close to the feasible region and/or the almost-optimal level set.
		This contrasts with other complexity bounds for convex optimization that rely on data-based condition numbers or algebraic measures, and that do not take into account any a priori reference point information.
	papers.ssrn.com /sol3/papers.cfm?abstract_id=288134 (281 words)

	ECE 287A - Convex Optimization and Applications
		Moreover, it is possible to address certain hard, non-convex problems (combinatorial optimization, integer programming) using convex approximations that are more efficient than classical linear ones.
		Prior exposure to optimization (e.g., linear programming) helps but is not necessary.
		To develop convex optimization code, some high-level packages might be useful: YALMIP, CVX (containing many examples).
	cosmal.ucsd.edu /~gert/ECE287F06 (595 words)

	Linearly Constrained Global Optimization
		This unified approach is accomplished by converting the constrained optimization problem to an unconstrained optimization problem through a parametric representation of its feasible region.
		The emerging field of global optimization deals with decision models, in the (possible) presence of multiple local optima with typically, the number of local pseudo-solutions is unknown, and it can be quite large.
		A critical evaluation of the current literature on even local optimization solution algorithms with business applications reveals that their approaches are frequently too complex, computationally laborious, and difficult to implement.
	home.ubalt.edu /ntsbarsh/opre640a/nonlinear.htm (9370 words)

	EE364: Convex Optimization
		It will be several weeks into the course before it all makes sense to you, but you might want to download and install it now, and browse the user guide.
		Exposure to numerical computing, optimization, and application fields helpful but not required; the engineering applications will be kept basic and simple.
		Catalog description: Concentrates on recognizing and solving convex optimization problems that arise in engineering.
	www.stanford.edu /class/ee364 (1000 words)

	SAL- Numerical Analysis - Optimization
		The optimization problem is to find the values of the unknown variables that minimize or maximize the objective functions (affected by the unknown variables) possiblly under certain constraints.
		GENBLIS -- genetic optimization and bootstrapping of linear structures.
		Global (and Local) Optimization: it is a comprehensive archive of online information on global optimization, and somewhat less comprehensive on local optimization, collected by Arnold Neumaier.
	sal.jyu.fi /B/3/index.shtml (951 words)

	Farkas Lemma - Convex Optimization
		Let K be any closed convex cone and K* its dual, and let x and y belong to a vector space R. Then
		x is in K <=> y^T x >= 0 for all y in K* which is a simple translation of the Farkas lemma to the language of convex cones, and a generalization of the well-known Cartesian fact
		We extend this notion to determine membership to the positive semidefinite cone boundary in its intersection with an affine subset.
	www.convexoptimization.com /dattorro/farkas_lemma.html (158 words)

	Amazon.com: Convex Optimization: Books: Stephen Boyd,Lieven Vandenberghe (Site not responding. Last check: 2007-10-22)
		The focus is on recognizing convex optimization problems and then finding the most appropriate technique for solving them.
		In this introduction we give an overview of mathematical optimization, focusing on the special role of convex optimization.
		As the name implies, and also as the authors put in preface, it is about recognizing, formulating, and solving convex optimization problems.
	www.amazon.com /Convex-Optimization-Stephen-Boyd/dp/0521833787 (1203 words)

	EE 227A / STAT 260 Home Page
		An important subclass of optimization problems are convex programs, in which both the objective function to be minimized and the associated constraint set are convex.
		Convex programs also arise frequently as approximations or relaxations of inherently non-convex problems (e.g., integer programming and combinatorial optimization).
		The EECS distinguished colloquium this week is by Stephen Boyd on convex optimization; the talk is on Wed.
	www.eecs.berkeley.edu /~wainwrig/ee227a (1934 words)

	Textbook: Convex Analysis and Optimization
		A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems.
		A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization.
		A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions.
	www.athenasc.com /convexity.html (438 words)

	CVXOPT
		CVXOPT is a free software package for convex optimization based on the Python programming language.
		Its main purpose is to make the development of software for convex optimization applications straightforward by building on Python's extensive standard library and on the strengths of Python as a high-level programming language.
		(This affects previous code in which optional arguments were passed by position instead of by keyword.) A revised nonlinear convex optimization solver with a simpler calling sequence.
	www.ee.ucla.edu /~vandenbe/cvxopt (609 words)

	Amazon.com: Convex Analysis (Princeton Landmarks in Mathematics and Physics): Books: Ralph Tyrell Rockafellar (Site not responding. Last check: 2007-10-22)
		Optimization: Proceedings of the 9th Belgian-French-German Conference on Optimization Namur, September 7-11, 1998 (Lecture Notes in Economics and Mathematical Systems) by Van Hien Nguyen on 10 pages
		Advances in Convex Analysis and Global Optimization - Honoring the Memory of C. Caratheodory (1873-1950) (Nonconvex Optimization and Its Applications,...
		Convex Analysis (Princeton Landmarks in Mathematics and Physics) by Ralph Tyrell Rockafellar
	www.amazon.com /Analysis-Princeton-Landmarks-Mathematics-Physics/dp/0691015864 (1056 words)

	MOSEK ApS optimization software. The choice when reliability, speed, and support are important.
		is designed to solve large-scale mathematical optimization problems.
		MOSEK provides specialized solvers for linear programing, mixed integer programing and many types of nonlinear convex optimization problems.
		Announcing the upcoming Open Optimization Seminar, to be held September 26, 2006
	www.mosek.com (91 words)

	Convex Network Optimization (Site not responding. Last check: 2007-10-22)
		This is a relatively long-term project aimed at developing a parallel algorithm for solving highly non-linear convex network optimization problems of interest in physics.
		The student working on the project is Aleksandar Donev under the supervision of Dr. Phillip Duxbury.
		The latest and most up to date are slides from my longer presentation at the MOPTA conference.
	computation.pa.msu.edu /NO (246 words)

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