Application of Market Models to Network Equilibrium Problems

We present a general two-side market model with divisible commodities and price functions of participants. A general existence result on unbounded sets is obtained from its variational inequality re-formulation. We describe an extension of the network flow equilibrium problem with elastic demands and a new equilibrium type model for resource allocation problems in wireless communication networks, which appear to be particular cases of the general market model. This enables us to obtain new existence results for these models as some adjustments of that for the market model. Under certain additional conditions the general market model can be reduced to a decomposable optimization problem where the goal function is the sum of two functions and one of them is convex separable, whereas the feasible set is the corresponding Cartesian product. We discuss some versions of the partial linearization method, which can be applied to these network equilibrium problems.Comment: 18 pages, 3 table

A Non-Monotone Conjugate Subgradient Type Method for Minimization of Convex Functions

We suggest a conjugate subgradient type method without any line-search for minimization of convex non differentiable functions. Unlike the custom methods of this class, it does not require monotone decrease of the goal function and reduces the implementation cost of each iteration essentially. At the same time, its step-size procedure takes into account behavior of the method along the iteration points. Preliminary results of computational experiments confirm efficiency of the proposed modification.Comment: 11 page

Variational Inequality Type Formulations of General Market Equilibrium Problems with Local Information

We suggest a new approach to creation of general market equilibrium models involving economic agents with local and partial knowledge about the system and under different restrictions. The market equilibrium problem is then formulated as a quasi-variational inequality that enables us to establish existence results for the model in different settings. We also describe dynamic processes, which fall into information exchange schemes of the proposed market model. In particular, we propose an iterative solution method for quasi-variational inequalities, which is based on evaluations of the proper market information only in a neighborhood of the current market state without knowledge of the whole feasible set and prove its convergence.Comment: 22 page

Simplified Versions of the Conditional Gradient Method

We suggest simple modifications of the conditional gradient method for smooth optimization problems, which maintain the basic convergence properties, but reduce the implementation cost of each iteration essentially. Namely, we propose the step-size procedure without any line-search, and inexact solution of the direction finding subproblem. Preliminary results of computational tests confirm efficiency of the proposed modifications.Comment: 20 page

Decentralized Multi-Agent Optimization Based on a Penalty Method

We propose a decentralized penalty method for general convex constrained multi-agent optimization problems. Each auxiliary penalized problem is solved approximately with a special parallel descent splitting method. The method can be implemented in a computational network where each agent sends information only to the nearest neighbours. Convergence of the method is established under rather weak assumptions. We also describe a specialization of the proposed approach to the feasibility problem.Comment: 26 page

Counter Attack on Byzantine Generals: Parameterized Model Checking of Fault-tolerant Distributed Algorithms

We introduce an automated parameterized verification method for fault-tolerant distributed algorithms (FTDA). FTDAs are parameterized by both the number of processes and the assumed maximum number of Byzantine faulty processes. At the center of our technique is a parametric interval abstraction (PIA) where the interval boundaries are arithmetic expressions over parameters. Using PIA for both data abstraction and a new form of counter abstraction, we reduce the parameterized problem to finite-state model checking. We demonstrate the practical feasibility of our method by verifying several variants of the well-known distributed algorithm by Srikanth and Toueg. Our semi-decision procedures are complemented and motivated by an undecidability proof for FTDA verification which holds even in the absence of interprocess communication. To the best of our knowledge, this is the first paper to achieve parameterized automated verification of Byzantine FTDA

Temperature dependence of the Laminar burning velocity of methanol flames

To better understand and predict the combustion behavior of methanol in engines, sound knowledge of the effect of the pressure, unburned mixture temperature, and composition on the laminar burning velocity is required. Because many of the existing experimental data for this property are compromised by the effects of flame stretch and instabilities, this study was aimed at obtaining new, accurate data for the laminar burning velocity of methanol–air mixtures. Non-stretched flames were stabilized on a perforated plate burner at 1 atm. The heat flux method was used to determine burning velocities under conditions when the net heat loss from the flame to the burner is zero. Equivalence ratios and initial temperatures of the unburned mixture ranged from 0.7 to 1.5 and from 298 to 358 K, respectively. Uncertainties of the measurements were analyzed and assessed experimentally. The overall accuracy of the burning velocities was estimated to be better than ±1 cm/s. In lean conditions, the correspondence with recent literature data was very good, whereas for rich mixtures, the deviation was larger. The present study supports the higher burning velocities at rich conditions, as predicted by several chemical kinetic mechanisms. The effects of the unburned mixture temperature on the laminar burning velocity of methanol were analyzed using the correlation uL = uL0(Tu/Tu0)α. Several published expressions for the variation of the power exponent α with the equivalence ratio were compared against the present experimental results and calculations using a detailed oxidation kinetic model. Whereas most existing expressions assume a linear decrease of α with an increasing equivalence ratio, the modeling results produce a minimum in α for slightly rich mixtures. Experimental determination of α was only possible for lean to stoichiometric mixtures and a single data point at equivalence ratio= 1.5. For these conditions, the measurement data agree with the modeling results