Arkadii V. Kryazhimskii

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A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration(More)
In this paper we investigate a class of nonlinear infinite horizon optimal control problems arising in mathematical economics in consideration of economic growth problems and problems of innovations dynamics. First order necessary optimality conditions in a form of the Pontryagin maximum principle are developed together with some extra conditions on the(More)
This paper (motivated by recent works on optimization of long-term economic growth) suggests some further developments in the theory of first-order necessary optimality conditions for problems of optimal control with infinite time horizons. We describe an approximation technique involving auxiliary finite-horizon optimal control problems and use it to prove(More)
We provide steps towards a welfare analysis of a two-country endogenous growth model where a relatively small follower absorbs part of the knowledge generated in the leading country. To solve a suitably defined dynamic optimisation problem an appropriate version of the Pontryagin maximum principle is developed. The properties of optimal controls and the(More)
The proposed approach to the insurance of regionally distributed property against high risk catastrophes is based on finding statistically robust coverages of the insurance companies. Such coverages guarantee that all companies survive no matter what scenario of the catastrophe from a given set of scenarios takes place. We describe a sequential algorithm(More)
For a class of infinite-dimensional minimization problems with nonlinear equality constraints, an iterative algorithm for finding global solutions is suggested. A key assumption is the convexity of the “epigraph”, a set in the product of the image spaces of the constraint and objective functions. A convexification method involving randomization is used. The(More)
Our basic model is a noncooperative multi-player game in which the governments of neighboring countries trade emission reductions. We prove the existence of a market equilibrium (combining properties of Pareto and Nash equilibria) and study algorithms of searching a market equilibrium. The algorithms are interpreted as repeated auctions in which the(More)
The paper presents a dynamic model of trading on market of patents. It is assumed that each firm participating in market produces its own technologies, whereas its manufacturing sector utilizes both originally produced technologies and those produced in other firms. The firms are therefore interdependent through the technology stocks used in manufacturing,(More)