The lagrange approach to infinite linear programs

Gabriel, J. Rigoberto; Martínez, Raquel R. López; Lerma, Onésimo Hernández

doi:10.1007/bf02579088

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…The proof of upper-bound is given below. Since we have (47) From the definition of constant , we have (48) As a result, where the last inequality is because of (47) and (48). This completes the proof.…”

Section: Appendix G Proof Of Theoremmentioning

confidence: 56%

“…As a remark, note that the per-stage delay penalty and perstage packet drop penalty are regular cost functions as defined in [46], [47]. The proof of the statement (b) is given as follows.…”

Section: Claim A-2mentioning

confidence: 99%

“…1) Let denote a global system state, and be the global system state space and action space, be an ergodic occupation measure [46] associated with a randomized policy. Then, Problem 1 is equivalent to the following problem [46]: IDLP This problem belongs to the infinite-dimensional linear programming, where the condition of strong duality has been studied already [47]. 2) Since is closed and convex (see [ 3) Let be the saddle point of the following Lagrangian:…”

Section: Claim A-2mentioning

confidence: 99%

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Delay-Aware Two-Hop Cooperative Relay Communications via Approximate MDP and Stochastic Learning

Wang

Lau

2013

IEEE Trans. Inform. Theory

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In this paper, a low-complexity delay-aware cross-layer scheduling algorithm for two-hop relay communication systems is proposed. The complex interactions of the queues at the source node and the relay nodes (RSs) are modeled as an infinite horizon average reward Markov decision process (MDP), whose state space involves the joint queue state information (QSI) of the queues at the source node and the RSs as well as the joint channel state information (CSI) of all S-R and R-D links. To address the curse of dimensionality, an equivalent MDP formulation is first proposed, where the system state depends only on global QSI. Furthermore, using approximate MDP and stochastic learning, an auction-based distributed online learning algorithm is derived, where each node iteratively estimates a per-node value function based on real-time observations of the local CSI and local QSI as well as signaling between relays. The combined distributed learning converges almost surely to a global optimal solution for large arrivals. Finally, it is showed by simulations that the proposed scheme achieves significant gain compared with various baselines such as the conventional CSIT-only control and the throughput optimal control (in stability sense).

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Section: Appendix G Proof Of Theoremmentioning

confidence: 56%

Section: Claim A-2mentioning

confidence: 99%

Section: Claim A-2mentioning

confidence: 99%

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Delay-Aware Two-Hop Cooperative Relay Communications via Approximate MDP and Stochastic Learning

Wang

Lau

2013

IEEE Trans. Inform. Theory

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“…This is a different and yet related infinite dimensional linear program (see also Gabriel, López-Martínez, and Hernández-Lerma 2001). As in Anderson and Nash (1987), the solvability of problem (D) cannot be settled using an argument similar to that in Theorem A.1 because the space of continuous functions on a compact set is not the dual of any normed space.…”

Section: Proof the Positive Cone Ofmentioning

confidence: 99%

Competitive equilibrium with search frictions: A general equilibrium approach

Jerez¹

2014

Journal of Economic Theory

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When the trading process is characterized by search frictions, traders may be rationed so markets need not clear. We build a general equilibrium model with transferable utility where the uncertainty arising from rationing is incorporated in the definition of a commodity, in the spirit of the Arrow-Debreu theory. Prices of commodities then depend not only on their physical characteristics, but also on the probability that their trade is rationed. The standard definition of competitive equilibrium is extended by replacing market clearing with a matching condition which describes a trading technology that is not frictionless. This condition relates the rationing probabilities of buyers and sellers to ratio of buyers to sellers in the market via an exogenous matching function with constant returns, as in standard search-theoretic models. When search frictions vanish, our model is equivalent to the competitive assignment model of Gretsky, Ostroy and Zame (1992). We adopt their approach, which uses linear programming techniques and duality theory, to derive the welfare and existence theorems in our search environment. Our competitive equilibrium notion is equivalent to that of directed (or competitive) search. The strength of our formulation and the linear programming approach is that they allow us to generalize the constrained efficiency and existence results in the directed search literature to a much broader class of economies. Our framework also opens the door to the use of linear programming algorithms for computing equilibria.Journal of Economic Literature Classification Numbers: D50, D61, D83.

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Dynamic costs and moral hazard: A duality-based approach

Arie

2016

Journal of Economic Theory

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The lagrange approach to infinite linear programs

Abstract: Infinite linear programs, convex problems, Lagrange approach, strong duality, 90C46, 90C25, 90C08,

Cited by 5 publications

References 19 publications

Delay-Aware Two-Hop Cooperative Relay Communications via Approximate MDP and Stochastic Learning

Delay-Aware Two-Hop Cooperative Relay Communications via Approximate MDP and Stochastic Learning

Competitive equilibrium with search frictions: A general equilibrium approach

Dynamic costs and moral hazard: A duality-based approach

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