Pub Date : 2023-10-25DOI: 10.1007/s00186-023-00833-0
Yanyun Liu, Baiqing Sun
{"title":"Investment strategies of duopoly firms with asymmetric time-to-build under a jump-diffusion model","authors":"Yanyun Liu, Baiqing Sun","doi":"10.1007/s00186-023-00833-0","DOIUrl":"https://doi.org/10.1007/s00186-023-00833-0","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"54 12","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135112634","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-10-03DOI: 10.1007/s00186-023-00839-8
Łukasz Kruk
Abstract We introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.
{"title":"A singular stochastic control problem with direction switching cost","authors":"Łukasz Kruk","doi":"10.1007/s00186-023-00839-8","DOIUrl":"https://doi.org/10.1007/s00186-023-00839-8","url":null,"abstract":"Abstract We introduce a new class of singular stochastic control problems in which the process controller not only chooses the push intensity, at a price proportional to the displacement caused by his action, but he can also change the allowable control direction, paying a fixed cost for each such switching. Singular control of the one-dimensional Brownian motion with quadratic instantaneous cost function and costly direction switching on the infinite time horizon is analyzed in detail, leading to a closed-form solution. This example is used as an illustration of qualitative differences between the class of problems considered here and classic singular stochastic control.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135739025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-29DOI: 10.1007/s00186-023-00838-9
Luis H. R. Alvarez E., Wiljami Sillanpää
Abstract We consider a class of stochastic optimal stopping and impulse control problems where the agent solving the problem anticipates that a regime switch will happen at a random time in the future. We assume that there are only two regimes, the regime switching time is exponentially distributed, the underlying stochastic process is a linear, regular, time-homogeneous diffusion in both regimes and the payoff may be regime-dependent. This is in contrast with most existing literature on the topic, where regime switching is modulated by a continuous-time Markov chain and the underlying process and payoff belong to the same parametric family in all regimes. We state a set of easily verifiable sufficient conditions under which the solutions to these problems are given by one-sided threshold strategies. We prove uniqueness of the thresholds and characterize them as solutions to certain algebraic equations. We also study how anticipation affects optimal policies i.e. we present various comparison results for problems with and without regime switching. It may happen that the anticipative value functions and optimal policies coincide with the usual ones even if the regime switching structure is non-trivial. We illustrate our results with practical examples.
{"title":"Optimal stopping and impulse control in the presence of an anticipated regime switch","authors":"Luis H. R. Alvarez E., Wiljami Sillanpää","doi":"10.1007/s00186-023-00838-9","DOIUrl":"https://doi.org/10.1007/s00186-023-00838-9","url":null,"abstract":"Abstract We consider a class of stochastic optimal stopping and impulse control problems where the agent solving the problem anticipates that a regime switch will happen at a random time in the future. We assume that there are only two regimes, the regime switching time is exponentially distributed, the underlying stochastic process is a linear, regular, time-homogeneous diffusion in both regimes and the payoff may be regime-dependent. This is in contrast with most existing literature on the topic, where regime switching is modulated by a continuous-time Markov chain and the underlying process and payoff belong to the same parametric family in all regimes. We state a set of easily verifiable sufficient conditions under which the solutions to these problems are given by one-sided threshold strategies. We prove uniqueness of the thresholds and characterize them as solutions to certain algebraic equations. We also study how anticipation affects optimal policies i.e. we present various comparison results for problems with and without regime switching. It may happen that the anticipative value functions and optimal policies coincide with the usual ones even if the regime switching structure is non-trivial. We illustrate our results with practical examples.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135200132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-28DOI: 10.1007/s00186-023-00837-w
Nguyen Ngoc Hai, Le Dung Muu, Bui Van Dinh
{"title":"An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand","authors":"Nguyen Ngoc Hai, Le Dung Muu, Bui Van Dinh","doi":"10.1007/s00186-023-00837-w","DOIUrl":"https://doi.org/10.1007/s00186-023-00837-w","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"68 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135386460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-27DOI: 10.1007/s00186-023-00836-x
Cristina Bazgan, Arne Herzel, Stefan Ruzika, Clemens Thielen, Daniel Vanderpooten
Abstract It is well known that, under very weak assumptions, multiobjective optimization problems admit $$(1+varepsilon ,dots ,1+varepsilon )$$ (1+ε,⋯,1+ε) -approximation sets (also called $$varepsilon $$ ε -Pareto sets ) of polynomial cardinality (in the size of the instance and in $$frac{1}{varepsilon }$$ 1ε ). While an approximation guarantee of $$1+varepsilon $$ 1+ε for any $$varepsilon >0$$ ε>0 is the best one can expect for singleobjective problems (apart from solving the problem to optimality), even better approximation guarantees than $$(1+varepsilon ,dots ,1+varepsilon )$$ (1+ε,⋯,1+ε) can be considered in the multiobjective case since the approximation might be exact in some of the objectives. Hence, in this paper, we consider partially exact approximation sets that require to approximate each feasible solution exactly, i.e., with an approximation guarantee of 1, in some of the objectives while still obtaining a guarantee of $$1+varepsilon $$ 1+ε in all others. We characterize the types of polynomial-cardinality, partially exact approximation sets that are guaranteed to exist for general multiobjective optimization problems. Moreover, we study minimum-cardinality partially exact approximation sets concerning (weak) efficiency of the contained solutions and relate their cardinalities to the minimum cardinality of a $$(1+varepsilon ,dots ,1+varepsilon )$$ (1+ε,⋯,1+ε) -approximation set.
{"title":"Approximating multiobjective optimization problems: How exact can you be?","authors":"Cristina Bazgan, Arne Herzel, Stefan Ruzika, Clemens Thielen, Daniel Vanderpooten","doi":"10.1007/s00186-023-00836-x","DOIUrl":"https://doi.org/10.1007/s00186-023-00836-x","url":null,"abstract":"Abstract It is well known that, under very weak assumptions, multiobjective optimization problems admit $$(1+varepsilon ,dots ,1+varepsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -approximation sets (also called $$varepsilon $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ε</mml:mi> </mml:math> -Pareto sets ) of polynomial cardinality (in the size of the instance and in $$frac{1}{varepsilon }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mfrac> <mml:mn>1</mml:mn> <mml:mi>ε</mml:mi> </mml:mfrac> </mml:math> ). While an approximation guarantee of $$1+varepsilon $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:math> for any $$varepsilon >0$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>ε</mml:mi> <mml:mo>></mml:mo> <mml:mn>0</mml:mn> </mml:mrow> </mml:math> is the best one can expect for singleobjective problems (apart from solving the problem to optimality), even better approximation guarantees than $$(1+varepsilon ,dots ,1+varepsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> can be considered in the multiobjective case since the approximation might be exact in some of the objectives. Hence, in this paper, we consider partially exact approximation sets that require to approximate each feasible solution exactly, i.e., with an approximation guarantee of 1, in some of the objectives while still obtaining a guarantee of $$1+varepsilon $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> </mml:mrow> </mml:math> in all others. We characterize the types of polynomial-cardinality, partially exact approximation sets that are guaranteed to exist for general multiobjective optimization problems. Moreover, we study minimum-cardinality partially exact approximation sets concerning (weak) efficiency of the contained solutions and relate their cardinalities to the minimum cardinality of a $$(1+varepsilon ,dots ,1+varepsilon )$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>,</mml:mo> <mml:mo>⋯</mml:mo> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mi>ε</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> -approximation set.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135536171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-09DOI: 10.1007/s00186-023-00835-y
Alexander Belyi, Stanislav Sobolevsky, Alexander Kurbatski, Carlo Ratti
Abstract We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.
{"title":"Subnetwork constraints for tighter upper bounds and exact solution of the clique partitioning problem","authors":"Alexander Belyi, Stanislav Sobolevsky, Alexander Kurbatski, Carlo Ratti","doi":"10.1007/s00186-023-00835-y","DOIUrl":"https://doi.org/10.1007/s00186-023-00835-y","url":null,"abstract":"Abstract We consider a variant of the clustering problem for a complete weighted graph. The aim is to partition the nodes into clusters maximizing the sum of the edge weights within the clusters. This problem is known as the clique partitioning problem, being NP-hard in the general case of having edge weights of different signs. We propose a new method of estimating an upper bound of the objective function that we combine with the classical branch-and-bound technique to find the exact solution. We evaluate our approach on a broad range of random graphs and real-world networks. The proposed approach provided tighter upper bounds and achieved significant convergence speed improvements compared to known alternative methods.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136108419","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-02DOI: 10.1007/s00186-023-00828-x
G. Eichfelder, Leo Warnow
{"title":"A hybrid patch decomposition approach to compute an enclosure for multi-objective mixed-integer convex optimization problems","authors":"G. Eichfelder, Leo Warnow","doi":"10.1007/s00186-023-00828-x","DOIUrl":"https://doi.org/10.1007/s00186-023-00828-x","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"8 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82195324","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-08-02DOI: 10.1007/s00186-023-00832-1
C. G. Higuera-Chan, Leonardo R. Laura-guarachi, J. Minjárez‐Sosa
{"title":"Stochastic Mitra–Wan forestry models analyzed as a mean field optimal control problem","authors":"C. G. Higuera-Chan, Leonardo R. Laura-guarachi, J. Minjárez‐Sosa","doi":"10.1007/s00186-023-00832-1","DOIUrl":"https://doi.org/10.1007/s00186-023-00832-1","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"31 1","pages":"169 - 203"},"PeriodicalIF":1.2,"publicationDate":"2023-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77030565","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-19DOI: 10.1007/s00186-023-00826-z
G. Eichfelder, T. Gerlach, Leo Warnow
{"title":"A test instance generator for multiobjective mixed-integer optimization","authors":"G. Eichfelder, T. Gerlach, Leo Warnow","doi":"10.1007/s00186-023-00826-z","DOIUrl":"https://doi.org/10.1007/s00186-023-00826-z","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"23 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77173909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-13DOI: 10.1007/s00186-023-00829-w
Kousik Das, S. K. Samanta
{"title":"Correction to: Computational analysis of GI[X] /D-MSP(a,b) /1 queueing system via RG-factorization","authors":"Kousik Das, S. K. Samanta","doi":"10.1007/s00186-023-00829-w","DOIUrl":"https://doi.org/10.1007/s00186-023-00829-w","url":null,"abstract":"","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"46 1","pages":"41 - 41"},"PeriodicalIF":1.2,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86567369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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