Showing papers on "Convex optimization published in 1987"

Interior-Point Polynomial Algorithms in Convex Programming

Abstract: Written for specialists working in optimization, mathematical programming, or control theory The general theory of path-following and potential reduction interior point polynomial time methods, interior point methods, interior point methods for linear and quadratic programming, polynomial time methods for nonlinear convex programming, efficient computation methods for control problems and variational inequalities, and acceleration of path-following methods are covered In this book, the authors describe the first unified theory of polynomial-time interior-point methods Their approach provides a simple and elegant framework in which all known polynomial-time interior-point methods can be explained and analyzed; this approach yields polynomial-time interior-point methods for a wide variety of problems beyond the traditional linear and quadratic programs The book contains new and important results in the general theory of convex programming, eg, their "conic" problem formulation in which duality theory is completely symmetric For each algorithm described, the authors carefully derive precise bounds on the computational effort required to solve a given family of problems to a given precision In several cases they obtain better problem complexity estimates than were previously known Several of the new algorithms described in this book, eg, the projective method, have been implemented, tested on "real world" problems, and found to be extremely efficient in practice Contents : Chapter 1: Self-Concordant Functions and Newton Method; Chapter 2: Path-Following Interior-Point Methods; Chapter 3: Potential Reduction Interior-Point Methods; Chapter 4: How to Construct Self- Concordant Barriers; Chapter 5: Applications in Convex Optimization; Chapter 6: Variational Inequalities with Monotone Operators; Chapter 7: Acceleration for Linear and Linearly Constrained Quadratic Problems

Lectures on modern convex optimization

Abstract: Sun, 06 Jan 2019 10:24:00 GMT lectures on modern convex optimization pdf Convex optimization problems arise frequently in many different fields. A comprehensive introduction to the subject, this book shows in detail how such problems can ... Mon, 07 Jan 2019 07:24:00 GMT Amazon.com: Convex Optimization, With Corrections 2008 ... Resources for Mathematics, mostly research and university level Sat, 05 Jan 2019 10:32:00 GMT Mathematics by Classifications mathontheweb.org Linear programming (LP, also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose ... Mon, 12 Feb 2001 23:53:00 GMT Linear programming Wikipedia A polytope may be convex. The convex polytopes are the simplest kind of polytopes, and form the basis for several different generalizations of the concept of polytopes. Thu, 27 Dec 2018 02:58:00 GMT Polytope Wikipedia Lectures (HTF) refers to Hastie, Tibshirani, and Friedman's book The Elements of Statistical Learning (SSBD) refers to Shalev-Shwartz and Ben-David's book ... Thu, 03 Jan 2019 23:28:00 GMT Foundations of Machine Learning bloomberg.github.io Box and Cox (1964) developed the transformation. Estimation of any Box-Cox parameters is by maximum likelihood. Box and Cox (1964) offered an example in which the ... Sat, 05 Jan 2019 16:09:00 GMT Glossary of research economics econterms Object Recognition I: Context (oral) Object-Graphs for Context-Aware Category Discovery (PDF, project) Yong Jae Lee, Kristen Grauman Grouplet: a Structured Image ... Thu, 13 Sep 2018 07:04:00 GMT CVPR 2010 papers on the web Papers This is the homepage of Thierry Roncalli ... La convergence de la gestion traditionnelle et de la gestion alternative, d"une part, l'émergence de la gestion ... Fri, 04 Jan 2019 21:03:00 GMT Thierry Roncalli's Home Page Download 1,250 free online courses from the world's top universities -Stanford, Yale, MIT, & more. Over 40,000 hours of free audio & video lectures. Sun, 23 Dec 2018 23:55:00 GMT 1,300 Free Online Courses from Top Universities | Open Culture DAMASK, micromechanical modeling,sheet forming, simulation, yield surface, crystal plasticity, CPFE, CPFEM, DAMASK, spectral solver, micromechanics, damage, Finite ... Fri, 07 Dec 2018 09:26:00 GMT Sheet Forming Simulations using Crystal Plasticity Finite ... This is the main resources page for the book Real-Time Rendering, Fourth Edition, by Tomas Akenine-Möller, Eric Haines, Naty Hoffman, Angelo Pesce, Micha&lstrok ... Mon, 07 Jan 2019 04:53:00 GMT Real-Time Rendering Resources Other writings: Darij Grinberg, On a double Sylvester determinant, unfinished draft. PDF file. Sourcecode of the paper. We prove the vanishing of a determinant whose ... Sat, 05 Jan 2019 05:03:00 GMT Darij Grinberg Algebra notes www.rz.ifi.lmu.de Electrical Engineering and Computer Science (EECS) spans a spectrum of topics from (i) materials, devices, circuits, and processors through (ii) control, signal ... Tue, 01 Jan 2019 12:10:00 GMT Department of Electrical Engineering and Computer Science ... 500 libros digitales PDF gratis matematica algebra lineal analisis funcional probabilidades topologia teoria de numeros estadistica calculo Tue, 01 Jan 2019 22:54:00 GMT 500 libros digitales gratis math books free download ... It is a great book for learning Probability theory. It assumes no background other than elementary mathematics. As of Jan. 2007 used copies are listed on Amazon at ... Sat, 05 Jan 2019 09:35:00 GMT Amazon.com: Fundamentals of Applied Probability Theory ... Os cursos universitários online grátis são

Conjugate Duality and Optimization

Abstract: The Role of Convexity and Duality Examples of Convex Optimization Problems Conjugate Convex Functions in Paired Spaces Dual Problems and Lagrangians Examples of Duality Schemes Continuity and Derivatives of Convex Functions Solutions to Optimization Problems Calculating Conjugates and Subgradients Integral Functionals

Discrete Convex Analysis

Abstract: A theory of “discrete convex analysis” is developed for integer-valued functions defined on integer lattice points. The theory parallels the ordinary convex analysis, covering discrete analogues of the fundamental concepts such as conjugacy, subgradients, the Fenchel min-max duality, separation theorems and the Lagrange duality framework for convex/nonconvex optimization. The technical development is based on matroid-theoretic concepts, in particular, submodular functions and exchange axioms. Sections 1–4 extend the conjugacy relationship between submodularity and exchange ability, deepening our understanding of the relationship between convexity and submodularity investigated in the eighties by A. Frank, S. Fujishige, L. Lovasz and others. Sections 5 and 6 establish duality theorems for M- and L-convex functions, namely, the Fenchel min-max duality and separation theorems. These are the generalizations of the discrete separation theorem for submodular functions due to A. Frank and the optimality criteria for the submodular flow problem due to M. Iri-N. Tomizawa, S. Fujishige, and A. Frank. A novel Lagrange duality framework is also developed in integer programming. We follow Rockafellar’s conjugate duality approach to convex/nonconvex programs in nonlinear optimization, while technically relying on the fundamental theorems of matroid-theoretic nature.

A Mathematical View of Interior-Point Methods in Convex Optimization

Abstract: This compact book, through the simplifying perspective it presents, will take a reader who knows little of interior-point methods to within sight of the research frontier, developing key ideas that were over a decade in the making by numerous interior-point method researchers. It aims at developing a thorough understanding of the most general theory for interior-point methods, a class of algorithms for convex optimization problems. The study of these algorithms has dominated the continuous optimization literature for nearly 15 years. In that time, the theory has matured tremendously, but much of the literature is difficult to understand, even for specialists. By focusing only on essential elements of the theory and emphasizing the underlying geometry, A Mathematical View of Interior-Point Methods in Convex Optimization makes the theory accessible to a wide audience, allowing them to quickly develop a fundamental understanding of the material.

Optimal time-varying flows on congested networks

Abstract: This paper develops a well-behaved convex programming model for least-cost flows on a general congested network on which flows vary over time, as for example during peak/off-peak demand cycles. The model differs from static network models and from most work on multiperiod network models because it treats the time taken to traverse each arc as varying with the flow rate on the arc. We develop extensions of the model to handle multiple destinations and multiple commodities, though not all of these extensions yield convex programs. As part of its solution, the model yields a set of nonnegative time-varying optimal flow controls for each arc. We determine and discuss sufficient conditions under which some or all of these optimal flow controls will be zero-valued. These conditions are consistent with computational experience. Finally, we indicate directions for further research.

Numerical methods for nondifferentiable convex optimization

Abstract: In this paper, we study in Section 1 the proximal method, within a nonexact form for nonsmooth programming. In Section 2 we give a new algorithm, related with the cutting plane method for minimizing on ℝ N a convex function that is a sum of a Legendre convex differentiable function and a nondifferentiable convex function. This algorithm is then used in Sections III and IV to solve nonsmooth convex optimization problems in the unconstrained and the constrained cases.

Iterative methods for large convex quadratic programs: a survey

Abstract: In this paper, we give a state-of-the-art review of many iterative methods for solving large convex quadratic programs. We attempt to classify several of the more basic methods in two categories, within each of which a unified iterative scheme will be introduced and its convergence analyzed. Hybrid iterative methods (such as the proximal point algorithm and a diagonalization scheme) that make use of the more basic schemes will also be described. The results of an extensive computer experimentation which is aimed at comparing the relative performance of the various methods will be reported and discussed. Finally, several important topics which require future research will be highlighted.

Relaxation methods for network flow problems with convex arc costs

Abstract: We consider the standard single commodity network flow problem with both linear and strictly convex possibly nondifferentiable arc costs. For the case where all arc costs are strictly convex we study the convergence of a dual Gauss-Seide! type relaxation method that is well suited for parallel computation. We then extend this method to the case where some of the arc costs are linear. As a special case we recover a relaxation method for the linear minimum cost network flow problem proposed in Bertsekas (1) and Bertsekas and Tseng (2).

Tolerances in computer-aided geometric design

Abstract: In the design of discrete part shapes, the specification of tolerance constraints can have major consequences for product quality and cost. Traditional methods for tolerance analysis and synthesis are time-consuming and have limited applicability. The thesis of this work is that geometric design systems based on solid modeling technology can be used to automate the solution of these problems. First, a mathematical theory of tolerances is developed. It is shown that a tolerance specification may be expressed as an "in-tolerance" region of a normed vector space over the reals. A representative selection of both dimensional (plus-minus) and geometric tolerance types is investigated. Using this theoretical framework, methods are developed for the solution of tolerance analysis and synthesis problems. Three methods for tolerance analysis are presented: a linear programming method, a Monte Carlo method, and a least squares fitting method. These methods differ as to linearity assumptions and computational costs. The linear programming method supports a worst-case solution basis. The other two methods also support the solution of tolerance analysis problems on a statistical basis. Next, models are developed for worst-case and statistical tolerance synthesis. It is shown that at least in some cases convex programming methods may be applicable. For both the analysis and the synthesis methods, all necessary geometric relationships are automatically derived from the geometric model. To provide a computational framework, a general strategy for constructive variational geometry is developed. This includes a general scheme for the relative positioning of parts and part features. Three relative positioning operators are described. Methods are given for the modeling of size, orientation, and position variations. Feasibility is demonstrated using an experimental geometric modeling system named GEOTOL. The linear programming and Monte Carlo methods are used in solving tolerance analysis problems for several simple assemblies, as well as for a larger bus bar assembly drawn from an actual product. It is shown that three-dimensional tolerancing problems can be solved by these methods.

Convex programming, variational inequalities, and applications to the traffic equilibrium problem

Abstract: The problem of determining the equilibrium distribution of the traffic flow in a city network is studied when the traffic demands on a set of given routes are known. The problem is formulated in terms of a nonlinear variational inequality over a polyhedron and a solving procedure, different from those shown in [1], [3], [4], is exhibited. This procedure is based on a very simple, necessary, and sufficient condition for a solution of the variational inequality to lie on a face of the polyhedron. Moreover, it is also compared, by means of numerical examples, with the procedures formulated in [1], [3], and [4] (see expressions (1.2) and (3.5) for a significant valuation).

Relaxation methods for problems with strictly convex separable costs and linear constraints

Abstract: We consider the minimization problem with strictly convex, possibly nondifferentiable, separable cost and linear constraints. The dual of this problem is an unconstrained minimization problem with differentiable cost which is well suited for solution by parallel methods based on Gauss-Seidel relaxation. We show that these methods yield the optimal primal solution and, under additional assumptions, an optimal dual solution. To do this it is necessary to extend the classical Gauss-Seidel convergence results because the dual cost may not be strictly convex, and may have unbounded level sets.

Proper efficiency and duality for vector valued optimization problems

Abstract: The duality results of Wolfe for scalar convex programming problems and some of the more recent duality results for scalar nonconvex programming problems are extended to vector valued programs. Weak duality is established using a ‘Pareto’ type relation between the primal and dual objective functions.

Second order necessary and sufficient conditions for convex composite NDO

Abstract: In convex composite NDO one studies the problem of minimizing functions of the formF:=h ○f whereh:ℝ m → ℝ is a finite valued convex function andf:ℝ n → ℝ m is continuously differentiable. This problem model has a wide range of application in mathematical programming since many important problem classes can be cast within its framework, e.g. convex inclusions, minimax problems, and penalty methods for constrained optimization. In the present work we extend the second order theory developed by A.D. Ioffe in [11, 12, 13] for the case in whichh is sublinear, to arbitrary finite valued convex functionsh. Moreover, a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature.

Penalty—proximal methods in convex programming

Abstract: An implementable algorithm for constrained nonsmooth convex programs is given. This algorithm combines exterior penalty methods with the proximal method. In the case of a linear program, the convergence is finite.

Convex Transformable Programming Problems and Invexity

Abstract: G. Heal has considered some properties of nonconvex porgramming problems which can be transformed into convex programming problems. In this paper we show that programming problems which can be transformed in such a way are a strict subset of invex programming problems. This has practical computational significance.

Approximate saddle-point theorems in vector optimization

Abstract: The paper contains definitions of different types of nondominated approximate solutions to vector optimization problems and gives some of their elementary properties. Then, saddle-point theorems corresponding to these solutions are presented with an application relative to approximate primal-dual pairs of solutions.

Outer Approximation by Polyhedral Convex Sets

Abstract: This paper deals with outer approximation methods for solving possibly multiextremal global optimization problems. A general theorem on convergence is presented and new classes of outer approximation methods using polyhedral convex sets are derived. The underlying theory is then related to the cut map-separator theory of Eaves and Zangwill. Two constraint dropping strategies are deduced.

A New CAD Method and Associated Architectures for Linear Controllers

Abstract: A new CAD method and associated architectures are proposed for linear controllers. The design method and architecture are based on recent results which parametrize all controllers which stabilize a given plant. With this architecture, the design of controllers is a convex programming problem which can be solved numerically. Constraints on the closed-loop system such as asymptotic tracking, decoupling, limits on peak excursions of variables, step response settling time and overshoot, as well as frequency domain inequalities are readily incorporated in the design. The minimization objective is quite general, with LQG, H ? , and new l 1 types as special cases. The constraints and objective are specified in a control specification language which is natural for the control engineer, referring directly to step responses, noise powers, transfer functions, and so on. This control specification language will be the input to a compiler which will translate the specifications into a standard convex program in RL, which is then solved by some numerical convex program solver. A small but powerful subset of the language has been specified and its associated compiler implemented. The architecture proposed not only makes design of the controller simple but also its implementation. These controllers can be built right now from off the shelf components or integrated using standard VLSI cells.

A constraint linearization method for nondifferentiable convex minimization

Abstract: This paper presents a readily implementable algorithm for solving constrained minimization problems involving (possibly nonsmooth) convex functions. The constraints are handled as in the successive quadratic approximations methods for smooth problems. An exact penalty function is employed for stepsize selection. A scheme for automatic limitation of penalty growth is given. Global convergence of the algorithm is established, as well as finite termination for piecewise linear problems. Numerical experience is reported.

Stability of Solutions to Convex Problems of Optimization

Abstract: Convex programming problem.- Convex optimal control problem subject to control constraints.- Convex optimal control problem subject to state and control constraints.- Differential stability of solutions to convex programming problems.- Differential stability of solutions to optimal control problems for discrete systems.- Differential stability of solutions to optimal control problems subject to control constraints.- Differential stability of solutions to optimal control problems subject to state and control constraints.

A mathematical convergence analysis of the convex linearization method for engineering design optimization

Abstract: This paper is concerned with the convex linearization method recently proposed by Fleury and Braibant for structural optimization. We give here a mathematical convergence analysis or this method. We also discuss some modifications of it.

An algorithm for maximizing a convex function over a simple set

Abstract: The problem of maximizing a convex function on a so-called simple set is considered. Based on the optimality conditions [19], an algorithm for solving the problem is proposed. This numerical algorithm is shown to be convergent. The proposed algorithm has been implemented and tested on a variety of test problems.

A generalization of the proximal point algorithm

Abstract: The problem that we consider in this paper is to find a solution to the generalized equation 0 ? T(x,y), where T is a maximal monotone operator on the product H1 × H2 of two Hilbert spaces H1 and H2. We give a generalization of the proximal map and the proximal point algorithm in which the proposed iterative procedure is based on just one variable. Applying to convex programming problems, instead of adding a quadratic term for all variables as in the proximal point algorithm, we add a quadratic term for a subset of variables. We prove that under a mild assumption our algorithm has the same convergence properties as the regular proximal point algorithm.

A general Farkas Lemma and characterization of optimality for a nonsmooth program involving convex processes

Abstract: In this paper, a generalization of the Farkas lemma is presented for nonlinear mappings which involve a convex process and a generalized convex function. Using this result, a complete characterization of optimality is obtained for the following nonsmooth programming problem: minimizef(x), subject to − ∈H(x) wheref is a locally Lipschitz function satisfying a generalized convexity hypothesis andH is a closed convex process.