Convexity - PowerPoint PPT Presentation

Explore the Progressive Hedging algorithm discussed in the Graduate Seminar on Operations Research. Topics include general framework, resource allocation examples, and handling non-convexity in decision-making. Dive into scenario decomposition and scenario-specific decision-making for well-hedged so

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Convex hulls are a fundamental concept in computational geometry, representing the smallest convex shape that contains a set of points. The process involves defining the convexity of a set, determining the unique convex polygon, and computing the convex hull efficiently using algorithms. This conten

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Explore the fundamentals of bond valuation, including the present value model and the yield model, to understand how bond prices are determined based on factors like market price, coupon payments, and yield to maturity. Learn about the price-yield curve, convexity, and how to calculate expected yiel

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Poverty traps theory, as proposed by Xavier Sala-i-Martin, explores the dynamics that keep countries in a cycle of poverty. It identifies three main traps: savings trap, non-convexity in production, and demographic trap. The theory suggests that to break out of poverty traps, countries may need incr

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Discussed are stochastic optimization problems, including convex-concave saddle point problems. Solutions like stochastic approximation and sample average approximation are analyzed. Theoretical assumptions and notations are explained, along with classical SA algorithms. Further discussions delve in

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Strategy optimization in geometric algorithms focusing on guessing a hidden card, data querying for quick retrieval, and intersection algorithms for polygons and polytopes in 2D and 3D spaces. Discussion on polygon representation, affine transformations, and convexity invariance.

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Explore the use of deep reinforcement learning for fully autonomous hybrid beamforming in mmWave massive MIMO systems, addressing non-convexity and non-linearity challenges. The approach involves interaction between agents and environments to update neural network parameters, optimizing system perfo

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Explore the concepts of convex functions and sets in Convex Optimization, including definitions, conditions of convexity, examples such as Softmax and Mutual Entropy, and their relation to convex sets. Learn about operations that preserve convexity, conjugate functions, log-concave/log-convex functi

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Dive into the world of mortgage backed securities (MBS) and credit enhancements with insights on different types of MBS, investor preferences, and various credit enhancement techniques. Explore the nuances of Agency Guarantees, CDOs, Convexity, Covered Bonds, and more, to enhance your knowledge in r

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Explore the fundamentals of convex optimization, including sets, functions, and problem statements. Learn about convexity, basic convex sets, separating hyperplanes, and dual cones. Understand how to define convex functions and sets, and examine the specifications and properties of convex sets in op

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An indifference curve is a graphical representation of all combinations of two goods that provide the same level of satisfaction to a consumer. The theory assumes rational behavior, ordinal utility, transitivity, consistency, and more. Properties of indifference curves include downward sloping, conv

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Explore the world of submodular functions, from their discrete analog of convexity/concavity to approximate learning techniques and positive results in valuation functions and beyond. Discover the potential applications in optimization and algorithmic game theory.

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Explore unconstrained minimization problems and strong convexity in convex optimization. Learn about Taylor expansion, Cauchy-Schwarz inequality, and optimization conditions for optimal solutions.

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Explore the intriguing concept of competitively chasing convex bodies in optimization theory. This research delves into the problem of selecting points within convex sets to minimize movement costs. Can deterministic algorithms compete with OPT, even when the latter anticipates the point selection i

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Explore the key concepts in convex optimization, including definitions of convexity, conditions of optimality, operations that preserve convexity, and examples of convex functions and sets. Learn about log-concave and log-convex functions, conjugate functions, and different views of functions and hy

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Explore the properties of convex, concave, and linear functions through graphical representations and mathematical equations. Understand the relationship between concavity, convexity, and linearity in functions, illustrated with examples and diagrams. Learn how to identify and distinguish between th

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