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18 Pages

### L22_dynrule

Course: GE 498 AN, Spring 2007
School: UIllinois
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Word Count: 1734

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22: Lecture Subgradient Methods April 11, 2007 Lecture 22 Outline Methods with Dynamic Stepsize Rule Directional Derivatives and Subgradients -Subgradients and -Subdifferentals Convex Optimization 1 Lecture 22 Method with Dynamic Stepsize with Known f General Assumption The function f (x) is convex and domf = Rn The set X is nonempty closed and convex Theorem Assume that General Assumption holds and...

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UIllinois - GE - 498 AN
Lecture 12: Necessary and Sufficient Conditions for Optimality of Primal-Dual PairsFebruary 28, 2007Lecture 12Outline General Form of Dual Problem Necessary and Sufficient Optimality Condition for Primal-Dual Pairs Karush-Kuhn-Tucker (KKT) C
UIllinois - GE - 498 AN
UIllinois - GE - 498 AN
Lecture 9: Convex ProblemsFebruary 19, 2007Lecture 9Outline Geometric Programming Semidefinite Programming Preliminary for Duality TheoryConvex Optimization1Lecture 9Geometric ProgrammingA Geometric Program is a problem of the follo
UIllinois - GE - 498 AN
Lecture 6: Closed FunctionsFebruary 5, 2007Lecture 6OutlineLog-Transformation Jensen's Inequality Level Sets Closed Functions Convexity and Continuity Recession Cone and Constancy Space Optimization TerminologyConvex Optimization 1Lecture 6
UIllinois - GE - 498 AN
Lecture 13: Duality and SensitivityMarch 5, 2007Lecture 13Outline Perturbed Primal Problem Primal Value Function Role in Sensitivity Role in Zero-Gap Duality and Problem ReformulationsConvex Optimization1Lecture 13Perturbed Problem
UIllinois - GE - 498 AN
Lecture 14: Algorithms Unconstrained OptimizationMarch 7, 2007Lecture 14Outline Terminology and Assumptions Gradient Descent Method Newton's MethodConvex Optimization1Lecture 14Unconstrained Minimizationminimize f (x) Assumptions:
UIllinois - GE - 498 AN
Lecture 15: Numerical Experiments with Algorithms for Unconstrained OptimizationMarch 12, 2007Lecture 15Outline Gradient Descent Method Sufficient Function Decrease Gradient and Newton's Method (Homework) Condition Number Affine Transforma
UIllinois - GE - 498 AN
Convex OptimizationInstructor: Angelia Nedich January 17, 2007Lecture 1Outline What is the Course About Who Cares and Why Course Objective Convex Optimization History New Interest in the Topic Formal IntroductionConvex Optimization1L
UIllinois - GE - 498 AN
Lecture 2: Convex setsJanuary 22, 2007Lecture 2OutlineVectors and Norms Convex set Cones Affine sets Half-Spaces, Hyperlanes, Polyhedra Ellipsoids and Norm Cones Convex, Conical, and Affine Hulls SimplexConvex Optimization 1Lecture 2Notat
UIllinois - GE - 498 AN
Lecture 3: Convex Set Topology and Operations Preserving ConvexityJanuary 24, 2007Lecture 3OutlineReview basic topology in Rn Open Set and Interior Closed Set and Closure Dual Cone Recession Directions of a Convex Set Lineality Space Convex Se
UIllinois - GE - 498 AN
Lecture 4: Operations Preserving Convexity Convex FunctionsJanuary 29, 2007Lecture 4OutlineRecession Cone Review Lineality Space Convex Set Decomposition More Operations Preserving Convexity Convex Functions Examples Verifying Convexity of a F
UIllinois - GE - 498 AN
Lecture 21: Subgradient MethodsApril 9, 2007Lecture 21Outline Subgradients and Level Sets Subgradient Method Convergence and Convergence RateConvex Optimization1Lecture 21Subgradients and Level SetsA vector s is a subgradient of a c
UIllinois - GE - 498 AN
Lecture 19: Convex Non-Smooth OptimizationApril 2, 2007Lecture 19Outline Convex non-smooth problems Examples Subgradients and subdifferentials Subgradient properties Operations with subgradients and subdifferentialsConvex Optimization1
UIllinois - GE - 498 AN
Lecture 18: Interior-Point MethodMarch 28, 2007Lecture 18Outline Barrier-type interior point method Phase I method Bound on number of Newton's iteration Limitations of interior point methodConvex Optimization1Lecture 18Inequality Co
UIllinois - GE - 498 AN
Lecture 7: Existence of SolutionsFebruary 7, 2007Lecture 7OutlineOptimization Terminology Issues in Optimization Existence of Solutions Implications and Applications Optimality ConditionConvex Optimization1Lecture 7Optimization Termino
UIllinois - GE - 498 AN
Lecture 8: Convex ProblemsFebruary 12, 2007Lecture 8OutlineRevisit Optimality Condition Unconstrained Problems Problems with Linear Constraints Problems with Inequalities and Equalities Linear-Fractional Programming Second-Order Cone Programmi
UIllinois - GE - 498 AN
Lecture 11: Strong Duality ResultsFebruary 26, 2007Lecture 11Outline Slater Condition and its Variations Convex Objective with Linear Inequality Constraints Quadratic Objective over Quadratic Constraints Recession Cone Conditions Represent
UIllinois - GE - 498 AN
Lecture 26: Badly Conditioned Convex ProblemsApril 25, 2007Lecture 26Outline Shor's space-dilation method [variable metric method] Tikhonov's regularization Nesterov's averaging algorithmConvex Optimization1Lecture 26Let f be convex
UIllinois - GE - 498 AN
Lecture 25: Efficiency of Proximal Bundle Method Variable Metric Subgradient MethodsApril 23, 2007Lecture 25Outline Computing -Subgradients Simplified Proximal Bundle Method Convergence Rate of the Method Subdifferential of a Composite Func
UIllinois - GE - 498 AN
Lecture 24: Steepest Descent Subgradient MethodsApril 18, 2007Lecture 24Outline -Subgradients and -Subdifferentals Bundle-Type Method using &quot;Cutting-Plane Idea&quot;Convex Optimization1Lecture 24-Subgradient and -Subdifferential An -subgr
UIllinois - GE - 498 AN
Lecture 17: Interior-Point MethodMarch 26, 2007Lecture 17Outline Review of Self-concordance Overview of Netwon's Methods for Equality Constrained Minimization Examples Interior-Point MethodConvex Optimization1Lecture 17Self-Concorda
UIllinois - GE - 498 AN
Lecture 5: Verifying Convexity Operations Preserving Convex FunctionsJanuary 31, 2007Lecture 5OutlineVerifying Convexity of a Function Operations on Functions Preserving Convexity Log-Transformation Jensen's Inequality Extended-Value Functions
UIllinois - GE - 498 AN
Lecture 10: Lagrangian DualityFebruary 21, 2007Lecture 10Outline Motivation Visualization of Primal-Dual Framework Primal-Dual Constrained Optimization Problems Dual Function Properties Weak and Strong Duality ExamplesConvex Optimizatio
UIllinois - GE - 498 AN
Lecture 20: Subgradients and Optimality ConditionsApril 4, 2007Lecture 20Outline Subgradients for Concave Problems Computing Subgradients in Dual Problems Optimality Conditions Cutting-Plane MethodsConvex Optimization1Lecture 20Subg
Villanova - THEO - 5990
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Villanova - THEO - 5990
Villanova - THEO - 5990
Villanova - THEO - 5990
Villanova - THEO - 5990
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in pes planus describe the talar bone and what happens to shoes.name the symptoms of pes planus.what would cause a spring ligament sprain?how many miles are a pair of shoes good for for running?what is the term for flat foot?describe the di
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