{"title":"On the Dual Gradient Descent Method for the Resource\nAllocation Problem in Multiagent Systems","authors":"D. B. Rokhlin","doi":"10.1134/S1990478924020133","DOIUrl":null,"url":null,"abstract":"<p> We consider a sequence of block-separable convex programming problems describing the\nresource allocation in multiagent systems. We construct several iterative algorithms for setting the\nresource prices. Under various assumptions about the utility functions and resource constraints,\nwe obtain estimates for the average deviation (regret) of the objective function from the optimal\nvalue and the constraint residuals. Here the average is understood as the expectation for\nindependent identically distributed data and as the time average in the online optimization\nproblem. The analysis of the problem is carried out by online optimization methods and duality\ntheory. The algorithms considered use the information concerning the difference between the total\ndemand and supply that is generated by agents’ reactions to prices and corresponds to the\nconstraint residuals.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 2","pages":"316 - 332"},"PeriodicalIF":0.5800,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924020133","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
We consider a sequence of block-separable convex programming problems describing the
resource allocation in multiagent systems. We construct several iterative algorithms for setting the
resource prices. Under various assumptions about the utility functions and resource constraints,
we obtain estimates for the average deviation (regret) of the objective function from the optimal
value and the constraint residuals. Here the average is understood as the expectation for
independent identically distributed data and as the time average in the online optimization
problem. The analysis of the problem is carried out by online optimization methods and duality
theory. The algorithms considered use the information concerning the difference between the total
demand and supply that is generated by agents’ reactions to prices and corresponds to the
constraint residuals.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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