Branch & Bound
I Identifies the solution to an integer problem through relaxation of integer constraints I For a non-integer optimal variable found in the relaxed problem, denotedx ˜, the problem is then split into two sub-problems constrained aroundx ˜,byx x˜ or x x˜ b c d e
D C C2C: : CA D C2 A :C , / DA: ) CD C A 2 Robust stationkeeping control on unstable orbits (Ken Oguri) NBA DraftKings optimal lineup selection ( C& : C: 2 2 : H C (2A : D 2C: & Greedy Results Sparse Optimization 2 CH CA2: C : : D C D C C2C: : 2 - 2 A :C (Cheryl Hansen, Nelson Mitchell, Tyler Schuessler)
: feasible region : feedback control !&'5 !&'5'( C C: 2 2 : H : uncertain state : state realization Will Shand
!& !&'(
pos. dev. at ! pos. dev. at ! "#$% reference trajectory &'() Greedy Algorithm How can we find the most important !" From www.gurobi.com/resources/getting-started/mip-basics Pr %&'( ∈ feasible ≥ 1 − 4& Sample Lineups Avg. Optimal f (x) Avg. Cost uncertainty reduced parts of a dataset, or make our methods by FB control Anthony Davis Cameron Payne Andre Roberson Cody Zeller Cody Zeller Anthony Davis robust to outliers? We can make use of the /A: : 2 H E A Sun Damion Lee Danilo Gallinari Cameron Payne C E A 2 H 2 : 2 2 A : 2C: Danilo Gallinari DeAndre Bembry Chandler Parsons 121.7736 $43, 460 notion of sparsity to solve problems like A: : 2 A & E Harrison Barnes DeMarcus Cousins Isaiah Canaan Isaiah Thomas Dorian Finney-Smith Jabari Parker these by creating an optimization problem Klay Thompson John Wall Tyson Chandler Mike Muscala Michael Carter-Williams Zach LaVine in which we only keep the most
1 fundamental components of our solution The minimum for a random starting value after for a variety of and throw out the remainder. learning rates was 159.3298. The above table was computed APPM 4720/5720using a learning (special rate of h =0 topics).0168 In this project, I look at methods for “Advanced Convex Optimization” solving sparse optimization problems, and apply them to background subtraction in Prof. Becker, fall 2018 video analysis. Optimizing Honey Bee Foraging Yield Student projects Sparse Optimization (background subtraction) through Efficient Waggle Dancing Student backgrounds: (Will Shand) (Richard Clancy, Liam Madden, Daniel Ferguson) ‣ Applied Math (BS, BS/MS, PhD) Optimizing Honey Bee Foraging Yield through Efficient Waggle Dancing ‣ Engineering Physics (BS) For our project, we investigated optimal parameter values to maximize the foraging yield of honey bees given two food sources. We solved the optimization problem via grid search, Nelder-Mead, a direct ‣ method, and the Adjoint State Method. Computer Science (BS) ‣ Business (PhD) Set Covering in Boulder (for mothership/drone problem) ‣ Aerospace (PhD) Set Covering in(Hasti Boulder: Rahemi Hasti and Sam Rahemi Zhang) & Sam Zhang Support Vector Clustering Support(Grant Vector Baker, Clustering Matt Maierhofer)
Grant Baker Matt Maierhofer
APPM 5720 Convex Optimization Fall 2018
Clustering on Tw o M oons Dataset
● Use support vector machine infrastructure to ⌫n d hypersph ere to en close all data in fe a tu r e s p a c e ● If lin e b e tw e e n p o in ts is e n tire ly w ith in hypersphere, points are in the sam e Hyperparameter Tuning Cluster Boundaries cluster ● Naive algorithm slow, but possible speedu p with stoch astic gradient an d red u ction of n u m b er of p oin ts to ch eck ● Perform s well only with ⌫ne hyperparam eter tuning (a) Greedy (b) Branch & Bound Blobs k-means Failure