arXiv subjects

I. V. Konnov

Publications and source records attributed to I. V. Konnov.

6 recordsLinked to original sources

arXiv2021

A little about models

We discuss several aspects of creation of adequate mathematical models in other sciences. In particular, many difficulties stem from great complexity of the source systems and the presence of a variety of uncertain factors. We illustrate the effect of uncertainty on the known consumer demand model. We conclude that not every uncertainty can be represented by a random variable, and that these concepts are not equivalent. We discuss also the role of different information concepts in mathematical models. We give additional illustrative examples of models of quite complex systems.

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arXiv2020

Decomposable Penalty Method for Generalized Game Problems with Joint Constraints

We consider an extension of a noncooperative game problem where players have joint binding constraints. In this case, justification of a generalized equilibrium point needs a reasonable mechanism for attaining this state. We suggest to combine a penalty method together with shares allocation of right-hand sides, which replaces the initial problem with a sequence of the usual Nash equilibrium problems together with an upper level variational inequality as a master problem. We show convergence of solutions of these auxiliary penalized problems to a solution of the initial game problem under weak coercivity conditions.

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arXiv2020

A General Class of Relative Optimization Problems

We consider relative or subjective optimization problems where the goal function and feasible set are dependent of the current state of the system under consideration. In general, they are formulated as quasi-equilibrium problems, hence finding their solutions may be rather difficult. We describe a rather general class of relative optimization problems in metric spaces, which in addition depend on the starting state. We also utilize quasi-equilibrium type formulations of these problems and show that they admit rather simple descent solution methods. This approach gives suitable trajectories tending to a relatively optimal state. We describe several examples of applications of these problems.

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arXiv2017

The Method of Pairwise Variations with Tolerances for Linearly Constrained Optimization Problems

We consider a method of pairwise variations for smooth optimization problems, which involve polyhedral constraints. It consists in making steps with respect to the difference of two selected extreme points of the feasible set together with special threshold control and tolerances whose values reduce sequentially. The method is simpler and more flexible than the well-known conditional gradient method, but keeps its useful sparsity properties and is very suitable for large dimensional optimization problems. We establish its convergence under rather mild assumptions. Efficiency of the method is confirmed by its convergence rates and results of computational experiments.

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arXiv2016

Selective Bi-coordinate Method for Non-Stationary and Non-Smooth Resource Allocation Type Problems

We propose a method of bi-coordinate variations for non-stationary and non-smooth optimization problems, which involve a single linear equality and box constraints. Here only approximation sequences are known instead of exact values of the cost function and parameters of the feasible set. It consists in making descent steps with respect to only two selected coordinates satisfying some special threshold rule. The method is simpler essentially than the usual gradient or dual type ones and differs from the previous known bi-coordinate ones suggested for the usual stationary and smooth problems. We establish its convergence under rather mild assumptions. Computational tests also reveal certain preferences of the proposed method over the known ones.

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arXiv2016

An Adaptive Partial Linearization Method for Optimization Problems on Product Sets

We suggest an adaptive version of a partial linearization method for composite optimization problems. The goal function is the sum of a smooth function and a non necessary smooth convex separable function, whereas the feasible set is the corresponding Cartesian product. The method consists in selective component-wise steps together with a special control of a tolerance sequence. This technique is destined to reduce the computational expenses per iteration and maintain the basic convergence properties. We also establish its convergence rates and describe some examples of applications. Preliminary results of computations illustrate usefulness of the new method.

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