Author
Vladimir I. Danilov
Other affiliations: Space Research Institute, Central Economics and Mathematics Institute, Tomsk Polytechnic University
Bio: Vladimir I. Danilov is an academic researcher from Russian Academy of Sciences. The author has contributed to research in topics: Plasticity & Autowave. The author has an hindex of 18, co-authored 165 publications receiving 1255 citations. Previous affiliations of Vladimir I. Danilov include Space Research Institute & Central Economics and Mathematics Institute.
Papers published on a yearly basis
Papers
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TL;DR: It turns out, that a main reason for the existence of an economy with many indivisible goods and one perfectly divisible good is that supplies and demands of indIVisible goods should be sets of a class of discrete convexity.
117 citations
TL;DR: In this article, the authors extend the theory of decision-making under uncertainty from a classical environment into a non-classical one, where the Boolean lattice of events is replaced by an arbitrary ortho-complemented poset.
Abstract: In this article, Savage's theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.
48 citations
TL;DR: In this article, a theory of discrete convexity for the lattice of integer points Z n, which is based on the separation property, was developed, and it is shown that these (maximal) classes are in one-to-one correspondence with pure systems.
45 citations
TL;DR: Some restrictions on preferences sufficient for existence of stable matching in multi-sided systems are given.
43 citations
TL;DR: In this article, the authors analyzed the features of plastic flow localization at all stages of strain hardening and at the prefracture stage, and showed that macroscopic localization of plasminar flow at these stages can be considered as a self-organization process.
Abstract: The features of plastic flow localization at all stages of strain hardening and at the prefracture stage were analyzed. It was shown that macroscopic localization of plastic flow at these stages can be considered as a self-organization process. At the linear hardening stage, an autowave process of flow localization occurs in the sample, which is characterized by the wavelength and propagation velocity. At the prefracture stage, the autowave process collapses with macroneck formation followed by the nucleation of a ductile crack.
42 citations
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Book•
01 Jan 1991
TL;DR: In this paper, the Lovasz Extensions of Submodular Functions are extended to include nonlinear weight functions and linear weight functions with continuous variables, and a Decomposition Algorithm is proposed.
Abstract: Introduction. 1. Mathematical Preliminaries. Submodular Systems and Base Polyhedra. 2. From Matroids to Submodular Systems. Matroids. Polymatroids. Submodular Systems. 3. Submodular Systems and Base Polyhedra. Fundamental Operations on Submodular Systems. Greedy Algorithm. Structures of Base Polyhedra. Intersecting- and Crossing-Submodular Functions. Related Polyhedra. Submodular Systems of Network Type. Neoflows. 4. The Intersection Problem. The Intersection Theorem. The Discrete Separation Theorem. The Common Base Problem. 5. Neoflows. The Equivalence of the Neoflow Problems. Feasibility for Submodular Flows. Optimality for Submodular Flows. Algorithms for Neoflows. Matroid Optimization. Submodular Analysis. 6. Submodular Functions and Convexity. Conjugate Functions and a Fenchel-Type Min-Max Theorem for Submodular and Supermodular Functions. Subgradients of Submodular Functions. The Lovasz Extensions of Submodular Functions. 7. Submodular Programs. Submodular Programs - Unconstrained Optimization. Submodular Programs - Constrained Optimization. Nonlinear Optimization with Submodular Constraints. 8. Separable Convex Optimization. Optimality Conditions. A Decomposition Algorithm. Discrete Optimization. 9. The Lexicographically Optimal Base Problem. Nonlinear Weight Functions. Linear Weight Functions. 10. The Weighted Max-Min and Min-Max Problems. Continuous Variables. Discrete Variables. 11. The Fair Resource Allocation Problem. Continuous Variables. Discrete Variables. 12. The Neoflow Problem with a Separable Convex Cost Function. References. Index.
505 citations
Book•
20 Mar 2013TL;DR: This book builds on the author’s prior research in this area, and also his practical experience of developing algorithms for matching kidney patients to donors in the UK, for assigning medical students to hospitals in Scotland, and for allocating students to elective courses and projects.
Abstract: Preliminary Definitions, Results and Motivation Stable Matching Problems: The Stable Marriage Problem: An Update SM and HR with Indifference The Stable Roommates Problem Further Stable Matching Problems Other Optimal Matching Problems: Pareto Optimal Matchings Popular Matchings Profile-Based Optimal Matchings.
488 citations
31 May 1993
TL;DR: Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization and on the application of techniques from combinational optimization to nonlinear problems.
Abstract: : Significant progress has been made with solution of location problems and in preprocessing and decomposition for discrete optimization. There has also been research on the application of techniques from combinational optimization to nonlinear problems.
421 citations
13 Jan 1978
TL;DR: This report briefly summarizes research on the following topics: game theory and energy; scheduling of large research and development programs; bimatrix games; cost/benefit analyses; measures of worth of weapons systems; hybrid primal algorithm; branch and round algorithm.
Abstract: : This report briefly summarizes research on the following topics: game theory and energy; scheduling of large research and development programs; bimatrix games; cost/benefit analyses; measures of worth of weapons systems; hybrid primal algorithm; branch and round algorithm. A listing of papers prepared and published is included. (Author)
340 citations