- 3 The Simplex Method 3.1 Preview of the simplex algorithm
- Instabilty of a Random Access Communication Channel
- Part II. LQG Models Lectures 711 have covered the LQG model and have thereby introduced various con-
- 10 Observability We present observability and the LQG model with process and observation noise.
- MATHEMATICAL TRIPOS Part III Wednesday 4 June, 2003 1:30 to 4:30
- 4 The Simplex Tableau 4.1 Choice of pivot column
- OPTIMIZATION AND CONTROL Richard Weber
- Lent Term 2001 Richard Weber Time Series --Examples Sheet
- `There are lies, damned lies, and statistics.' (Mark Twain)
- x n n I s n s S r r T q r t G t T r G T
- mality. Theorem (sufficient
- Circulation circulation
- OPTIMIZATION Contents Schedules
- 2 The Solution of LP Problems 2.1 Basic solutions
- Optimization and Control: Examples Sheet 3 Continuous-time Models
- Anchoring and Bias In the absence of hard data, a person's estimate of an
- 1 Dynamic Programming: The Optimality Equation We introduce the idea of dynamic programming and the principle of optimality. We
- characterisation constraints,
- Tripos Questions in Optimization IB (198598) Parts of some of these questions are no longer relevant to the syllabus. You should not be
- constraints constraints
- Easter 98 (April 16, 1998) Richard Weber D2: OPTIMIZATION
- 4 Positive Programming We address the special theory of maximizing positive rewards, (noting that there may
- Incentives for Large Peer-to-Peer Systems Costas Courcoubetis
- MATHEMATICAL TRIPOS Part III Monday, 31 May, 2010 1:30 pm to 4:30 pm
- MATHEMATICAL TRIPOS Part III Monday 2 June 2008 1.30 to 4.30
- MATHEMATICAL TRIPOS Part III Monday 4 June 2007 9.00 to 12.00
- MATHEMATICAL TRIPOS Part III Tuesday 1 June, 2004 13:30 to 16:30
- MATHEMATICAL TRIPOS Part III Thursday 30 May 2002 1.30 to 4.30
- MATHEMATICAL TRIPOS Part III Friday 1 June 2001 1.30 4.30
- 2 Some Examples of Dynamic Programming We illustrate the method of dynamic programming and some useful `tricks'.
- 3 Dynamic Programming over the Infinite Horizon We define the cases of discounted, negative and positive dynamic programming and
- 5 Negative Programming We address the special theory of minimizing positive costs, (noting that the action that
- 7 LQ Models We present the LQ regulation model in discrete and continuous time, the Riccati equa-
- 9 Infinite Horizon Limits We define stabilizability and discuss the LQ regulation problem over an infinite horizon.
- 13 Pontryagin's Maximum Principle We explain Pontryagin's maximum principle and give some examples of its use.
- adjoint variable, 49 average-cost, 21
- Optimization and Control: Examples Sheet 1 Lectures 15
- Solutions to Tripos Questions in Optimization and Control 1 In a Markov decision problem the state evolves stochastically as a function of only the current
- Prisoners' Dilemma Two cigarette companies each have the option of ad-
- The `find the oldest' problem A teacher knows that all n pupils in her class were
- A self-organising system N books are placed on a shelf. They have unknown
- A repeated game with hidden knowledge Consider the usual two person, zero-sum game, but
- The Ladies Nylon Stocking Problem A woman has a collection of n nylon stockings.
- Part III. Continuous Time Models Lectures 1216 have covered continuous time deterministic dynamic programming and
- Easter Term 2010 Richard Weber OPTIMIZATION
- Aims of this course . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii Schedules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
- Statistics Examples Sheet 3 This examples sheet covers material of the lectures 1116 and is appropri-
- 15 Controlled Markov Jump Processes We conclude with models for controlled optimization problems in a continuous-time
- 16 Controlled Diffusion Processes We give a brief introduction to controlled continuous-time stochastic models with a
- 5 Lagrangian Methods 5.1 The Lagrangian
- Programming equivalence
- MATHEMATICAL TRIPOS Part III Friday 3 June, 2005 9 to 12
- 11 Minimum Cost Circulation Problems 11.1 Sufficient conditions for a minimal cost circulation
- OPTIMIZATION AND CONTROL Richard Weber
- Tripos Questions in Statistics IB (198899) Let X1, . . . , X6 be a sample from the uniform distribution on [0, ] where [1, 2] is an
- 6 Average-cost Programming We address the infinite-horizon average-cost case, the optimality equation for this case
- 8 Controllability We define and give conditions for controllability in discrete and continuous time.
- saddlepoint simultaneously.
- OPTIMIZATION Contents Schedules
- Statistics Examples Sheet 1 This examples sheet covers material of the first 5 lectures and is appropri-
- 12 Transportation and Transshipment Problems 12.1 The transportation algorithm
- 10 Maximal Flow in a Network 10.1 Maxflow/mincut theory
- Anchoring and Bias In the absence of hard data, a person's estimate of an
- Feasible set for P x 1 \Gamma x 2 = 3
- 11 Kalman Filtering and Certainty Equivalence We presents the important concepts of the Kalman filter, certainty-equivalence and the
- Statistics Further Examples Sheet This examples sheet has some extra questions which you may like to do
- 1. L.C. Thomas, Games, Theory and Application, Wiley, Chich-ester (1984).
- Mathematics of Operational Research This course is accessible to a candidate with mathematical maturity who has
- 12 Dynamic Programming in Continuous Time We develop the HJB equation for dynamic programming in continuous time.
- An online Estimation Procedure for CellLoss Probabilities in ATM links
- 9 Two Person ZeroSum Games 9.1 Games with a saddlepoint
- TIME SERIES Syllabus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
- theoretical preliminary
- Part I. Dynamic Programming The first six lectures have covered deterministic and stochastic dynamic programming
- 6 The Lagrangian Dual 6.1 Example: further use of the Lagrangian sufficiency theorem
- MATHEMATICAL TRIPOS Part III Thursday 1 June 2006 1.30 to 4.30
- Mathematics for Operations Research 1. SOLUTION. The Lagrangian is
- Mathematics for Operations Research 1. SOLUTION. First we put a set of feasible flows on the tree of dashed arcs (shown
- Mathematics for Operations Research 1. SOLUTION. In (a) an equilibrium pair (saddle point) is for the row plyaer to
- Optimization and Control: Examples Sheet 1 Dynamic programming
- Optimization and Control: Examples Sheet 2 1. [lecture 7] Consider a scalar deterministic linear system, xt = Axt-1 + But-1, with
- Easter 99 Version 99.1 Colin Sparrow D2: Optimization
- Economic Issues in Shared Infrastructures Costas Courcoubetis
- Easter Term 2010 Richard Weber OPTIMIZATION
- Statistics Examples Sheet 2 This examples sheet covers material of lectures 610 and is appropriate
- OPTIMIZATION AND CONTROL Richard Weber
- The optimal strategy for symmetric rendezvous search on K3
- An Introduction to Large Deviations for Teletraffic Engineers
- Easter 2010 Richard Weber Optimization -Examples Sheet 1
- Tripos Questions in Optimization and Control 1 060229 A policy is to be chosen to maximize
- MATHEMATICAL TRIPOS Part III Friday 1 June 2001 1.30 4.30
- Maxflow/mincut replacements
- deviations? performance
- Mathematics for Operations Research 1. Consider the following constrained optimization problem.
- Mathematics for Operations Research 1. Solve the two-person zero-sum games with the payoff matrices (for player 1) of
- MATHEMATICAL TRIPOS Part III Friday, 29 May, 2009 1:30 pm to 4:30 pm
- 8 Algebra of Linear Programming 8.1 Basic feasible solutions and extreme points
- Transportation Transshipment
- Preliminaries Optimization
- Why study large deviations? ffl The performance of many systems is limited by events
- sufficiency constraint.
- BUFFER OVERFLOW ASYMPTOTICS FOR A BUFFER HANDLING MANY TRAFFIC SOURCES
- Easter 2010 Richard Weber Optimization -Examples Sheet 2
- Easter 98 (April 16, 1998) Richard Weber D2: OPTIMIZATION
- Search for a Moving Target An object moves back and forth between two locations
- Easter 98 (April 16, 1998) Richard We* D2: OPTIMIZATION
- Remarks. 1. iterations.
- Mathematics for Operations Research -1. Consider the uncapacitated network flow problem below. The label next to
- 14 Applications of the Maximum Principle We discuss the terminal conditions of the maximum principle and further examples of
- 7 Shadow Prices and Lagrangian Necessity 7.1 Sufficient conditions for optimality
- 1 Preliminaries 1.1 Optimization under constraints
- THE DISPUTED GARMENT PROBLEM: THE MATHEMATICS OF
- Paper 1, Section I 7H Statistics
- Paper 1, Section I 8H Optimization
- Paper 3, Section I 9H Markov Chains
- 1034 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 24, NO. 5, MAY 2006 Incentives for Large Peer-to-Peer Systems
- J. Appl. Prob. 33, 886-903 (1996) Printed in Israel
- BIN PACKING WITH DISCRETE ITEM SIZES, PART I: PERFECT PACKING THEOREMS AND THE AVERAGE CASE BEHAVIOR OF
- SCHEDULING STOCHASTIC JOIlS ON PARALLEL MACHINES TO HINHIIZE HAKESPi\N OR FLOWTIME
- MONOTONE OPTIMAL POLICIES FOR LEFT-SKIP-FREE MARKOV
- Therefore, if A andB are the two least valuable items, then bA*+ bZ< M where bA* and b* are the winning bids on items A and B. In this case any bidder can obtain
- A Self-Organizing Bin Packing Heuristic Janos Csirik David S. Johnson
- SIAM J.APPL. MATH. ? 1984 SocietyforIndustrialand AppliedMathematics Vol. 44, No. 4, August1984 015
- J. Appl.Prob.28, 852-861 (1990) Printedin Israel
- On Ruckle's conjecture on accumulation games
- J.Appl.Prob.23,841-847(1986) PrintedinIsrael
- Proceedlngs of 25th Conference on Declslon and Control
- Markov Chains These notes contain material prepared by colleagues who have also presented this course
- MATHEMATICAL TRIPOS: PART IB Michaelmas Term 2011 MARKOV CHAINS Richard Weber
- Dynamic Bandwidth Pricing: Provision Cost, Market Size, Effective Bandwidths and Price Games
- 1778 IEEE TRANSACTIONSON COMMUNICATIONS,VOL. 43, NO. 2/3/4, FEBRUARY/MARCH/APRIL 1995 Admission Control and Routing in ATM Networks
- Adv. Appl. Prob.24, 727-737 (1992) Printedin N. Ireland
- Markov Chains, Computer Proofs, and Average-Case Analysis of Best Fit Bin Packing
- Preprint 0 (2000) 1{22 1 Telecommunication Systems, 15(3-4):323-343, 2000
- Optimal Symmetric Rendezvous Search on Three Locations Richard Weber
- Paper 2, Section II 29K Optimization and Control
- Adv. Appl. Prob. 23, 429-430 (1991) Printedin N. Ireland
- In IFIP TC6 International Conference on Broadband Communications (BC'98), Stuttgart, Germany, April 1-3, 1998
- Optimal Scheduling of Peer-to-Peer File Dissemination Jochen Mundinger
- J. Appl. Prob.16, 690-695 (1979) Printedin Israel
- Adv. Appl. Prob.19, 177-201(1987) Printedin N. Ireland
- In International Conference on Telecommunications, Melbourne, Australia, April 2-4, 1997 ABR Pricing Experiments in a Real Network
- Indexability and Whittle Index for Restless Bandit Problems Involving Reset Processes
- To appear in RANDOM STRUCTURES AND ALGORITHMS Bin Packing with Discrete Item Sizes,
- Adv. Appl. Prob. 19, 454-473 (1987) Printedin N. Ireland
- ABCs of the Bomber Problem and its Relatives Richard Weber
- THE CAFETERIAPROCESS-TANDEM QUEUES WITH0-1 DEPENDENTSERVICETIMESAND THE
- Monotonic and Insensitive Optimal Policies for Control of Queues with Undiscounted Costs Author(s): Shaler Stidham Jr. and Richard R. Weber
- J. Appl.Prob.29, 667-681 (1992) Printedin Israel
- Queueing Systems 13(1993)291-314 291 A survey of Markov decision models for control
- Easter Term 2010 Richard Weber OPTIMIZATION
- On the Performance of an E ective Bandwidths Formula Costas Courcoubetis , George Fouskas
- Probability in the Engineering and Informational Sciences, 4, 1990, 19-27. Printed in the U.S.A. THE MOVE-TO-FRONT RULE
- A PROBLE~1 OF AM~l\JNITIO RATIONING At each time, s=0,1,2, ... there is a possibility that with
- Probability in the Engineering and Informational Sciences, 9, 1995, 285-296. Printed in the U.S.A. EFFECTIVE BANDWIDTHS FOR
- Pricing Resources on Demand Costas Courcoubetis, Sergios Soursos and Richard Weber
- STABILITYOF FLEXIBLEMANUFACTURINGSYSTEMS COSTAS COURCOUBETIS
- MEASUREMENT-BASED USAGE CHARGES IN COMMUNICATIONS NETWORKS
- Paper 1, Section I 8H Optimization
- DOMINANT STRATEGIES IN STOCHASTIC ALLOCATION AND SCHEDULING PROBLEMS
- J.Appl.Prob.23,989-999(1986) PrintedinIsrael
- Optimal Call Routing in VoIP Costas Courcoubetis
- MATHEMATICAL TRIPOS: PART IB Michaelmas Term 2011 MARKOV CHAINS Richard Weber
- SEQUENTIAL OPEN-LOOP SCHEDULING STRATEGIES P. Nash, R.R. Weber
- Probability in the Engineering and Informational Sciences, 4, 1990, 447-460. Printed in the U.S.A. STABILITY OF ON-LINE
- Analysis of Peer-to-Peer File Dissemination Jochen Mundinger
- Large Deviation and Fluid Approximations in Control
- Adv. Appl. Prob.19, 202-218 (1987) Printedin N. Ireland
- An on-line Estimation Procedure for Cell-Loss Probabilities in ATM links
- MATHEMATICAL TRIPOS Part III Monday, 6 June, 2011 1:30 pm to 4:30 pm
- Concavity and Monotonicity Properties in a Groundwater Management Model
- J. Appl.Prob.28, 839-851 (1990) PrintedinIsrael
- J. Appl.Prob.27, 637-648 (1990) Printedin Israel
- Asymptotics for Provisioning Problems of Peering Wireless LANs
- THE THEORY OF OPTIMAL STOPPING RICHARD Re WEBER
- Paper 3, Section I 9H Markov Chains
- J.Appl.Prob.23,708-717(1986) PrintedinIsrael
- Economic Issues in Shared Infrastructures Costas Courcoubetis and Richard Weber
- J.Appl.Prob.19,167-182(1982) PrintedinIsrael
- Tripos Questions in Optimization and Control 20 00314 In a television game show a contestant is successively asked questions Q1, . . . , Q9.
- 166 IEEE TRANSACTIONSONAUTOMATICCONTROL,VOL. 38,NO. 1,JANUARY1993 for k-a sufficiently large negative integer. Thus, by choosing
- Fundamental Discrepancies Between Average-Case Analyses Under Discrete and Continuous Distributions
- 950 Technical Notes EVANS,R. V. 1981.MarkovChainDesign Problems.Opns.Res.29, 959-970.
- J.R. Statist.Soc. B (1978), 40, No. 3,pp. 322-327
- STOCHASTIC SCHEDULING ON PARALLEL PROCESSORS AND MINIMIZATION OF CONCAVE FUNCTIONS
- On the Sum-of-Squares Algorithm for Bin Packing JANOS CSIRIK
- MATHEMATICAL TRIPOS: PART II Lent Term 2012 OPTIMIZATION AND CONTROL Richard Weber
- The Two Cultures of Mathematics. W. T. Gowers
- MATHEMATICAL TRIPOS: PART II Lent Term 2012 OPTIMIZATION AND CONTROL Richard Weber
- 9 Dynamic Programming 9.2 The Value Iteration Algorithm for a
- Optimization and Control: Examples Sheet 1 Lectures 15
- Multi-armed Bandits and the Gittins Richard Weber
- MATHEMATICAL TRIPOS: PART II Lent Term 2012 OPTIMIZATION AND CONTROL Richard Weber
- Paper 2, Section II 29K Optimization and Control
- Optimization and Control Table of Contents i