-
作者：Schied, A
作者单位：Technical University of Berlin
摘要：This paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model, where the robust utility functional is defined by a set Q of probability measures. Our main result shows that this problem can often be reduced to determining a least favorable measure Q(0) is an element of Q, which is universal in the sense that it does not depend on the particular utility function. The robust problem ...
-
作者：Lian, ZT; Liu, LM; Neuts, MF
作者单位：University of Macau; Hong Kong University of Science & Technology; University of Arizona
摘要：We consider a discrete-time (s, S) inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventory-level process. We obtain a closed-form expected cost function. Numerical results demonstrate some properties of optimal ordering policies and cost functions. When c...
-
作者：He, YR; Sun, J
作者单位：Sichuan Normal University; National University of Singapore; Massachusetts Institute of Technology (MIT); National University of Singapore; Nanyang Technological University; Singapore-MIT Alliance for Research & Technology Centre (SMART)
摘要：Error bounds for cone inclusion problems in Banach spaces are established under conditions weaker than Robinson's constraint qualification. The results allow the cone to be more general than the origin and therefore also generalize a classical error bound result concerning equality-constrained sets in optimization. Applications in finite-dimensional differentiable inequalities and in tangent cones are discussed.
-
作者：Murota, K
作者单位：University of Tokyo
摘要：Multimodular functions and L-convex functions have been investigated almost independently, but they are, in fact, equivalent objects that can be related through a unimodular coordinate transformation. Some facts known for L-convex functions can be translated to new results for multimodular functions, and vice versa. In particular, the local optimality condition for global optimality found in the literature of multimodular functions should be rectified, and a discrete separation theorem holds f...
-
作者：Popescu, I
作者单位：INSEAD Business School
摘要：We provide an optimization framework for computing optimal upper and lower bounds on functional expectations of distributions with special properties, given moment constraints. Bertsimas and Popescu (Optimal inequalities in probability theory: a convex optimization approach. SIAM J Optim. 2004. Forthcoming) have already shown how to obtain optimal moment inequalities for arbitrary distributions via semidefinite programming. These bounds are not sharp if the underlying distributions possess add...
-
作者：Mannor, S; Tsitsiklis, JN
作者单位：McGill University; Massachusetts Institute of Technology (MIT)
摘要：We consider the empirical state-action frequencies and the empirical reward in weakly communicating finite-state Markov decision processes under general policies. We define a certain polytope and establish that every element of this polytope is the limit of the empirical frequency vector, under some policy, in a strong sense. Furthermore, we show that the probability of exceeding a given distance between the empirical frequency vector and the polytope decays exponentially with time under every...
-
作者：Dash, S
作者单位：International Business Machines (IBM); IBM USA
摘要：We examine the complexity of branch-and-cut proofs in the context of 0-1 integer programs. We establish an exponential lower bound on the length of branch-and-cut proofs that use 0-1 branching and lift-and-project cuts (called simple disjunctive cuts by some authors), Gomory-Chvatal cuts, and cuts arising from the No matrix-cut operator of Lovasz and Schrijver. A consequence of the lower-bound result in this paper is that branch-and-cut methods of the type described above have exponential runn...
-
作者：Ye, YY
作者单位：Stanford University
摘要：We present a new complexity result on solving the Markov decision problem (MDP) with n states and a number of actions for each state, a special class of real-number linear programs with the Leontief matrix structure. We prove that when the discount factor theta is strictly less than 1, the problem can be solved in at most O(n(1.5)(log1/(1 - theta) + log n)) classical interior-point method iterations and O(n(4)(log 1/(1 - theta) + log n)) arithmetic operations. Our method is a combinatorial int...
-
作者：Dokov, SP; Morton, DP
作者单位：University of Texas System; University of Texas Austin
摘要：We develop a class of lower bounds on the expectation of a convex function. The bounds utilize the first two moments of the underlying random variable, whose support is contained in a bounded interval or hyperrectangle. Our bounds have applications to stochastic programs whose random parameters are known only through limited-moment information. Computational results are presented for two-stage stochastic linear programs.
-
作者：Levy, AB
作者单位：Bowdoin College
摘要：Successive approximation methods appear throughout numerical optimization, where a solution to an optimization problem is sought as the limit of solutions to a succession of simpler approximation problems. Such methods include essentially any standard penalty method, barrier method, trust region method, augmented Lagrangian method, or sequential quadratic programming (SQP) method, as well as many other methods. The approximation problems on which a successive approximation method is based typi...
