PPT-Convex Sets & Concave Sets

A planar region is called convex if and only if for any pair of points in the line segment lies completely in   Otherwise it is called concave Convex  . Textbook Reference 10.3 (P.419-430). Learning Goals. Understand how to draw ray diagrams for concave mirrors. Be able to identify when images are real or virtual. Success Criteria. To draw at least one ray diagram for concave mirrors and to identify if the image is real or virtual.. Problems in Ramsey theory typically ask a question of the form: "how many elements of some structure must there be to guarantee that a particular property will hold?“. Here we consider geometric Ramsey-type results about finite point sets in the plane.. Origami World. David . Fouhey. , . Abhinav. Gupta, Martial Hebert. 1. 2. 3. Local Evidence. 4. Hoiem. et al. 2005, . Saxena. et al. 2005, . Fouhey. et al. 2013, etc.. Constraints. 5. Constraints for Single Image 3D. relaxations. via statistical query complexity. Based on:. V. F.. , Will Perkins, Santosh . Vempala. . . On the Complexity of Random Satisfiability Problems with Planted . Solutions.. STOC 2015. V. F.. Guo. . Qi, . Chen . Zhenghai. , Wang . Guanhua. , Shen . Shiqi. , . Himeshi. De Silva. Outline. Introduction: Background & Definition of convex . hull. Three . algorithms. Graham’s Scan. Jarvis March. Origami World. David . Fouhey. , . Abhinav. Gupta, Martial Hebert. 1. 2. 3. Local Evidence. 4. Hoiem. et al. 2005, . Saxena. et al. 2005, . Fouhey. et al. 2013, etc.. Constraints. 5. Constraints for Single Image 3D. for Sequential Game Solving. Overview. Sequence-form transformation. Bilinear saddle-point problems. EGT/Mirror . prox. Smoothing techniques for sequential games. Sampling techniques. Some experimental results. S4P1 Students will investigate the nature of light using tools such as mirrors, lenses, and prisms. ..  . c. . Identify the physical attributes of a convex lens, a concave lens, and a prism and where each is used. . . Hull. . Problemi. Bayram AKGÜL . &. Hakan KUTUCU. Bartın Üniversitesi. Bilgisayar Programcılığı. Bölümü. Karabük Üniversitesi. Bilgisayar . Mühendisliği. Bölümü. İçerik. Convex. http://. www.robots.ox.ac.uk. /~oval/. Slides available online http://. mpawankumar.info. Convex Sets. Convex Functions. Convex Program. Outline. Convex Set. x. 1. x. 2. λ. . x. 1. (1 - . λ. ) . Have fun! . Polygon or . Non-Polygon. If polygon, name it.. If non-polygon, explain it.. Gabe. Polygon, hexagon. Ben. Non-Polygon, not closed. Vincent. Non-Polygon, not a segment. Michael. Non-Polygon, not segments. Objectives. Study the basic components of an . optimization problem. .. Formulation of design problems as mathematical programming problems. . Define . stationary points . Necessary and sufficient conditions for the relative maximum of a function of a single variable and for a function of two variables. . Nicholas . Ruozzi. University of Texas at Dallas. Where We’re Going. Multivariable calculus tells us where to look for global optima, but our goal is to design algorithms that can actually find one!. Xinyuan Wang. 01/. 17. /20. 20. 1. Contents. Affine. . and. . convex. . sets. Example. . of. . convex. . sets. Key. . properties. . of. . convex. . sets. Proper . cone, dual cone and . generalized .