93 research outputs found
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
Reachability in Parameterized Systems: All Flavors of Threshold Automata
Threshold automata, and the counter systems they define, were introduced as a framework for parameterized model checking of fault-tolerant distributed algorithms. This application domain suggested natural constraints on the automata structure, and a specific form of acceleration, called single-rule acceleration: consecutive occurrences of the same automaton rule are executed as a single transition in the counter system. These accelerated systems have bounded diameter, and can be verified in a complete manner with bounded model checking.
We go beyond the original domain, and investigate extensions of threshold automata: non-linear guards, increments and decrements of shared variables, increments of shared variables within loops, etc., and show that the bounded diameter property holds for several extensions. Finally, we put single-rule acceleration in the scope of flat counter automata: although increments in loops may break the bounded diameter property, the corresponding counter automaton is flattable, and reachability can be verified using more permissive forms of acceleration
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