Papers by Dimitri Bertsekas
1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes, 1976
This paper presents a method of converting a stochastic optimal control problem into a determinis... more This paper presents a method of converting a stochastic optimal control problem into a deterministic one, where probability distributions on the state space of the stochastic model are taken as states in the deterministic model. Relations between policies and rewards of the two models are given and counterparts to known deterministic results are developed for the stochastic model. A novel feature of our framework is the enlargement of the set of admissible control laws to include universally measurable policies rather than only Borel measurable policies. This feature together with a new measurable selection theorem allow us to dispense with the notions of p-optimality of Blackwell and Strauch [11,6] and the notion of p-essential infimum of Striebel [12], and obtain all results in a form comparable to that for deterministic problems.
Mathematical Programming Studies, 1982
It is well known 2, 3, 16 that if(T): R n® R n ̄ T: R^ n → R^ n is a Lipschitz continuous, strong... more It is well known 2, 3, 16 that if(T): R n® R n ̄ T: R^ n → R^ n is a Lipschitz continuous, strongly monotone operator and X is a closed convex set, then a solution x*∈ X of the variational inequality (xx*)¢(T)(x*)\ geqslant 0 (xx^*)'̄ T (x^*)\ geqslant 0,∨ x∈ X can be ...
1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes, 1978
ABSTRACT
... The permission of The Institute of Management Sciences to include this material is gratefully... more ... The permission of The Institute of Management Sciences to include this material is gratefully acknowledged. Finally we wish to thank Rose Harris and Dee Wrather for their excellent typing of the manuscript. XHI Page 15. This page intentionally left blank Page 16. ...
Lecture Notes in Control and Information Sciences, 1986
ABSTRACT Bibliography: p. 43-45. "October, 1984." (Revision of LIDS-P-1342) &am... more ABSTRACT Bibliography: p. 43-45. "October, 1984." (Revision of LIDS-P-1342) " NSF-ECS-8217668" " ONR/N00014-75-C-1183" " ONR-N00014-77-C-0532(NR041-519)" ONR N00014-84-K-0519" Dimitri P. Bertsekas, John N. Tsitsiklis, Michael Athans.
1986 25th IEEE Conference on Decision and Control, 1986
We introduce a cost function D which is meant to penalize con-ABSTRACT, gestion (large flows) thr... more We introduce a cost function D which is meant to penalize con-ABSTRACT, gestion (large flows) through each link. In particular, we assume We consider the behavior of distributed asynchronous routing althe separable form gorithms for optimizing the flows in a virtual circuit data network,= -
Proceedings of the 3rd international conference on Supercomputing - ICS '89, 1989
cations, it is natural to consider distributed exe-We consider iterative algorithms of the form x... more cations, it is natural to consider distributed exe-We consider iterative algorithms of the form x := cutions of this iteration whereby the ith processor f (x), executed by a parallel or distributed computupdates xi according to the formula ing system. We focus on asynchronous implementations whereby each processor iterates on a dif-,
Operations Research/Computer Science Interfaces Series, 1998
7 PLAY SELECTION IN AMERICAN FOOTBALL: A CASE STUDY IN NEURO-DYNAMIC PROGRAMMING Stephen D. Patek... more 7 PLAY SELECTION IN AMERICAN FOOTBALL: A CASE STUDY IN NEURO-DYNAMIC PROGRAMMING Stephen D. Patek1 and Dimitri P. Bertsekas2 1 Laboratory for Information and Decision Systems Massachusetts Institute of Technology Cambridge, Massachusetts 02139 sdpatek@ mit. ...
IEEE Transactions on Communications, 1984
SIAM Journal on Optimization, 1994
An extension of the proximal minimization algorithm is considered where only some of the minimiza... more An extension of the proximal minimization algorithm is considered where only some of the minimization variables appear in the quadratic proximal term. The resulting iterates are interpreted in terms of the iterates of the standard algorithm, and a uniform descent property is shown that holds independently of the proximal terms used. This property is used to give simple convergence proofs of parallel algorithms where multiple processors simultaneously execute proximal iterations using different partial proximal terms. It is also shown that partial proximal minimization algorithms are dual to multiplier methods with partial elimination of constraints, and a relation is established between parallel proximal minimization algorithms and parallel constraint distribution algorithms.
Page 1. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 34, NO. 6, JUNE 1989 589 Adaptive Aggregatio... more Page 1. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 34, NO. 6, JUNE 1989 589 Adaptive Aggregation Methods for Infinite Horizon Dynamic Programming DIMITRI P. BERTSEKAS, FELLOW, IEEE, AND DAVID A. CASTARON, MEMBER, IEEE ...
Journal of Heuristics, 1999
Page 1. Journal of Heuristics, 5, 89108 (1999) c 1999 Kluwer Academic Publishers, Boston. Manufa... more Page 1. Journal of Heuristics, 5, 89108 (1999) c 1999 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands. Rollout Algorithms for Stochastic Scheduling Problems DIMITRI P. BERTSEKAS* Department of ...
Advances in Parallel Computing, 1995
In this paper we consider a special type of trajectory optimization problem that can be viewed as... more In this paper we consider a special type of trajectory optimization problem that can be viewed as a continuous-space analog of the classical shortest path problem. This problem is approached by space discretization and solution of a discretized version of the associated Hamilton-Jacobi equation. It was recently shown by Tsitsiklis 1] that some of the ideas of classical shortest path methods, such as those underlying Dijkstra's algorithm, can be applied to solve the discretized Hamilton-Jacobi equation. In more recent work, Polymenakos, Bertsekas, and Tsitsiklis 2] have carried this analogy further to show that some e cient label correcting methods for shortest path problems, the SLF and SLF/LLL methods of 3] and 4], can be fruitfully adapted to solve the discretized Hamilton-Jacobi equation. In this paper we discuss parallel asynchronous implementations of these methods on a shared memory multiprocessor, the Alliant FX/80. Our results show that these methods are well suited for parallelization and achieve excellent speedup.
Models, Methods and Decision Support for Management, 2001
ABSTRACT We study the problem of shipping a set of products from a supplier to a customer in the ... more ABSTRACT We study the problem of shipping a set of products from a supplier to a customer in the supply chain. Each product is made available at the supplier at a given constant rate and absorbed by the customer on the basis of a given probability distribution of the customer demand. An inventory cost is charged at the supplier and at the customer if the level of the inventory is positive and a penalty cost is charged at the customer if the demand exceeds the inventory on hand. Shipments from the supplier to the customer are performed by vehicles of given capacity which generate a fixed cost per journey. The aim is to find a shipping strategy that minimizes the total expected discounted cost over an infinite horizon. This problem is a sequential decision making problem under uncertainty which belongs to the class of problems that can be solved by dynamic programming techniques. We implement the well known Policy iteration algorithm in order to obtain the optimal solution of the problem. Then, we propose two heuristic algorithms based on neuro-dynamic programming techniques and show their effectiveness on a set of randomly generated problem instances.
Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), 1998
... not be known in closed form. Then the exact or approximate computation of the rollout control... more ... not be known in closed form. Then the exact or approximate computation of the rollout control jik (F) using Eq. (8) becomes an important and nontrivial is-sue, since we need for all U E U(x) the value of Qk(5, U ) = E{g(X, %W ...
In this paper we develop parallel asynchronous implementations of some known and some new label c... more In this paper we develop parallel asynchronous implementations of some known and some new label correcting methods for finding a shortest path from a single origin to all the other nodes of a directed graph. We compare these implementations on a shared memory multiprocessor, the Alliant FX/80, using several types of randomly generated problems. Excellent (sometimes superlinear) speedup is achieved
ORSA Journal on Computing, 1993
ABSTRACT
Studies in Computational Mathematics, 2001
1971 IEEE Conference on Decision and Control, 1971
ABSTRACT
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Papers by Dimitri Bertsekas