{"title":"IMPLEMENTING ARROW–DEBREU EQUILIBRIA IN APPROXIMATELY COMPLETE SECURITY MARKETS","authors":"Koji Kusuda","doi":"10.15807/jorsj.67.18","DOIUrl":"https://doi.org/10.15807/jorsj.67.18","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140473696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is usually used to implement Ramaswami's recursion for the stationary distribution in M/G/1-type Markov chains. The main result of this paper is a subgeometric convergence formula for the total-variation distance between the stationary distribution and its LI truncation approximation.
{"title":"A SUBGEOMETRIC CONVERGENCE FORMULA FOR TOTAL-VARIATION ERROR OF THE LEVEL-INCREMENT TRUNCATION APPROXIMATION OF M/G/1-TYPE MARKOV CHAINS","authors":"Katsuhisa Ouchi, Hiroyuki Masuyama","doi":"10.15807/jorsj.66.243","DOIUrl":"https://doi.org/10.15807/jorsj.66.243","url":null,"abstract":"This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is usually used to implement Ramaswami's recursion for the stationary distribution in M/G/1-type Markov chains. The main result of this paper is a subgeometric convergence formula for the total-variation distance between the stationary distribution and its LI truncation approximation.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135928357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, we propose a new approach to strictly convex quadratic programming based on differential geometry. Broadly, our approach is an interior-point method. However, it can also be viewed as Newton's method on a Riemannian manifold on a set of interior points. In contrast to existing works on Newton's method on Riemannian manifolds, we introduce a parameterized metric and a retraction on the manifold, which are required to find a descent direction on the tangent space and update the solution on the manifold, respectively. The parameter of the metric is chosen at each iteration to preserve the local geodesic convexity of the objective function, while the retraction is designed to guarantee local convergence of the algorithm. The convergence rate is proven to be quadratic. Furthermore, we propose a modified algorithm emphasizing effective performance, which is numerically illustrated to be computationally as efficient as the primal-dual interior-point method, which has been widely used in practice. Our approach is also capable of warm start, which are preferable for model predictive control.
{"title":"A RIEMANNIAN-GEOMETRICAL APPROACH TO STRICTLY CONVEX QUADRATIC PROGRAMMING WITH CONVEXITY-PRESERVING METRIC PARAMETERIZATION","authors":"Toshihiro Wada, Toshiyuki Ohtsuka","doi":"10.15807/jorsj.66.219","DOIUrl":"https://doi.org/10.15807/jorsj.66.219","url":null,"abstract":"In this study, we propose a new approach to strictly convex quadratic programming based on differential geometry. Broadly, our approach is an interior-point method. However, it can also be viewed as Newton's method on a Riemannian manifold on a set of interior points. In contrast to existing works on Newton's method on Riemannian manifolds, we introduce a parameterized metric and a retraction on the manifold, which are required to find a descent direction on the tangent space and update the solution on the manifold, respectively. The parameter of the metric is chosen at each iteration to preserve the local geodesic convexity of the objective function, while the retraction is designed to guarantee local convergence of the algorithm. The convergence rate is proven to be quadratic. Furthermore, we propose a modified algorithm emphasizing effective performance, which is numerically illustrated to be computationally as efficient as the primal-dual interior-point method, which has been widely used in practice. Our approach is also capable of warm start, which are preferable for model predictive control.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135928353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A HYBRID ALGORITHM FOR THE ADWORDS PROBLEM","authors":"Iori Moriyama, S. Mizuno","doi":"10.15807/jorsj.66.176","DOIUrl":"https://doi.org/10.15807/jorsj.66.176","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47784161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"MIXED-INTEGER DC PROGRAMMING BASED ALGORITHMS FOR THE CIRCULAR PACKING PROBLEM","authors":"Y. Ikebe, Satoru Masuda, Takayuki Okuno","doi":"10.15807/jorsj.66.153","DOIUrl":"https://doi.org/10.15807/jorsj.66.153","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44668880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"KERNELIZATION ALGORITHMS FOR A GENERALIZATION OF THE COMPONENT ORDER CONNECTIVITY PROBLEM","authors":"Masataka Shirahashi, Naoyuki Kamiyama","doi":"10.15807/jorsj.66.112","DOIUrl":"https://doi.org/10.15807/jorsj.66.112","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43224863","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EX ANTE USER EQUILIBRIUM OF CAPACITATED NETWORKS","authors":"Y. Masuda, Tomohiro Shigemasa","doi":"10.15807/jorsj.66.130","DOIUrl":"https://doi.org/10.15807/jorsj.66.130","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41646744","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"EFFECT OF ROAD PRICING ON TRAFFIC VOLUME AND TOLL REVENUE IN GRID NETWORK","authors":"M. Miyagawa","doi":"10.15807/jorsj.66.142","DOIUrl":"https://doi.org/10.15807/jorsj.66.142","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43479788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study twelve stochastic input models for online problems and reveal the differences between their competitive ratios for the models. The competitive ratio is defined as the worst ratio between the expected optimal value and the expected profit of the solution obtained by the online algorithm, where the input distribution is restricted according to the input model. Our purpose is to clarify the difference among the input models from the view of the competitive ratio. To handle a broad class of online problems, we use a framework called request-answer games, which were introduced by Ben-David et al. The stochastic input models fit into two categories: known distribution and unknown distribution. We consider six natural classes of distribution for each category: dependent distributions, deterministic input, independent distributions, identical independent distribution, random order of a deterministic input, and random order of independent distributions. Using each input model, we consider two fundamental online problems, which are variants of the secretary problem and the prophet inequality problem. We use these problems to observe the difference in the competitive ratios of each input model.
{"title":"STOCHASTIC INPUT MODELS FOR ONLINE COMPUTING","authors":"Yasushi Kawase","doi":"10.15807/jorsj.66.95","DOIUrl":"https://doi.org/10.15807/jorsj.66.95","url":null,"abstract":"In this paper, we study twelve stochastic input models for online problems and reveal the differences between their competitive ratios for the models. The competitive ratio is defined as the worst ratio between the expected optimal value and the expected profit of the solution obtained by the online algorithm, where the input distribution is restricted according to the input model. Our purpose is to clarify the difference among the input models from the view of the competitive ratio. To handle a broad class of online problems, we use a framework called request-answer games, which were introduced by Ben-David et al. The stochastic input models fit into two categories: known distribution and unknown distribution. We consider six natural classes of distribution for each category: dependent distributions, deterministic input, independent distributions, identical independent distribution, random order of a deterministic input, and random order of independent distributions. Using each input model, we consider two fundamental online problems, which are variants of the secretary problem and the prophet inequality problem. We use these problems to observe the difference in the competitive ratios of each input model.","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135668603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"APPROXIMATION ALGORITHM FOR STEINER TREE PROBLEM WITH NEIGHBOR-INDUCED COST","authors":"Yusuke Kobayashi, Ryoga Mahara","doi":"10.15807/jorsj.66.18","DOIUrl":"https://doi.org/10.15807/jorsj.66.18","url":null,"abstract":"","PeriodicalId":51107,"journal":{"name":"Journal of the Operations Research Society of Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47659370","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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