By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.
{"title":"Axiomatic results and dynamic processes for two weighted indexes under fuzzy transferable-utility behavior","authors":"Y. Liao","doi":"10.3934/naco.2021047","DOIUrl":"https://doi.org/10.3934/naco.2021047","url":null,"abstract":"By considering the supreme-utilities and the weights simultaneously under fuzzy behavior, we propose two indexes on fuzzy transferable-utility games. In order to present the rationality for these two indexes, we define extended reductions to offer several axiomatic results and dynamics processes. Based on different consideration, we also adopt excess functions to propose alternative formulations and related dynamic processes for these two indexes respectively.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86893948","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}
Public bike sharing systems have become the most popular shared economy application in transportation. The convenience of this system depends on the availability of bikes and empty racks. One of the major challenges in operating a bike sharing system is the repositioning of bikes between rental sites to maintain sufficient bike inventory in each station at all times. Most systems hire trucks to conduct dynamic repositioning of bikes among rental sites. We have analyzed a commonly used repositioning scheme and have demonstrated its ineffectiveness. To realize a higher quality of service, we proposed a crowdsourced dynamic repositioning strategy: first, we analyzed the historical rental data via the random forest algorithm and identified important factors for demand forecasting. Second, considering 30-minute periods, we calculated the optimal bike inventory via integer programming for each rental site in each time period with a sufficient crowd for repositioning bikes. Then, we proposed a minimum cost network flow model in a time-space network for calculating the optimal voluntary rider flows for each period based on the current bike inventory, which is adjusted according to the forecasted demands. The results of computational experiments on real-world data demonstrate that our crowdsourced repositioning strategy may reduce unmet rental demands by more than 30% during rush hours compared to conventional trucks.
{"title":"A crowdsourced dynamic repositioning strategy for public bike sharing systems","authors":"I-Lin Wang, Chen-Tai Hou","doi":"10.3934/naco.2021049","DOIUrl":"https://doi.org/10.3934/naco.2021049","url":null,"abstract":"Public bike sharing systems have become the most popular shared economy application in transportation. The convenience of this system depends on the availability of bikes and empty racks. One of the major challenges in operating a bike sharing system is the repositioning of bikes between rental sites to maintain sufficient bike inventory in each station at all times. Most systems hire trucks to conduct dynamic repositioning of bikes among rental sites. We have analyzed a commonly used repositioning scheme and have demonstrated its ineffectiveness. To realize a higher quality of service, we proposed a crowdsourced dynamic repositioning strategy: first, we analyzed the historical rental data via the random forest algorithm and identified important factors for demand forecasting. Second, considering 30-minute periods, we calculated the optimal bike inventory via integer programming for each rental site in each time period with a sufficient crowd for repositioning bikes. Then, we proposed a minimum cost network flow model in a time-space network for calculating the optimal voluntary rider flows for each period based on the current bike inventory, which is adjusted according to the forecasted demands. The results of computational experiments on real-world data demonstrate that our crowdsourced repositioning strategy may reduce unmet rental demands by more than 30% during rush hours compared to conventional trucks.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86290935","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":"Stochastic DDM with regime–switching process","authors":"Battulga Gankhuu","doi":"10.3934/naco.2022031","DOIUrl":"https://doi.org/10.3934/naco.2022031","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81429025","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}
Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets begin{document}$ Oleft(sqrt{n} log(n) log(frac{n}{varepsilon}) right) $end{document}, iteration complexity bound for large-update methods with the special choice of its parameters.
Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets begin{document}$ Oleft(sqrt{n} log(n) log(frac{n}{varepsilon}) right) $end{document}, iteration complexity bound for large-update methods with the special choice of its parameters.
{"title":"Complexity analysis of an interior-point algorithm for linear optimization based on a new parametric kernel function with a double barrier term","authors":"Ayache Benhadid, F. Merahi","doi":"10.3934/naco.2022003","DOIUrl":"https://doi.org/10.3934/naco.2022003","url":null,"abstract":"<p style='text-indent:20px;'>Kernel functions play an important role in the complexity analysis of the interior point methods (IPMs) for linear optimization (LO). In this paper, an interior-point algorithm for LO based on a new parametric kernel function is proposed. By means of some simple analysis tools, we prove that the primal-dual interior-point algorithm for solving LO problems meets <inline-formula><tex-math id=\"M1\">begin{document}$ Oleft(sqrt{n} log(n) log(frac{n}{varepsilon}) right) $end{document}</tex-math></inline-formula>, iteration complexity bound for large-update methods with the special choice of its parameters.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90222697","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":"Static Markowitz mean-variance portfolio selection model with long-term bonds","authors":"Dennis Ikpe, Romeo Mawonike, F. Viens","doi":"10.3934/naco.2022030","DOIUrl":"https://doi.org/10.3934/naco.2022030","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83688274","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, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [1,2] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.
{"title":"Global optimality conditions and duality theorems for robust optimal solutions of optimization problems with data uncertainty, using underestimators","authors":"J. Kerdkaew, R. Wangkeeree, R. Wangkeeree","doi":"10.3934/naco.2021053","DOIUrl":"https://doi.org/10.3934/naco.2021053","url":null,"abstract":"In this paper, a robust optimization problem, which features a maximum function of continuously differentiable functions as its objective function, is investigated. Some new conditions for a robust KKT point, which is a robust feasible solution that satisfies the robust KKT condition, to be a global robust optimal solution of the uncertain optimization problem, which may have many local robust optimal solutions that are not global, are established. The obtained conditions make use of underestimators, which were first introduced by Jayakumar and Srisatkunarajah [1,2] of the Lagrangian associated with the problem at the robust KKT point. Furthermore, we also investigate the Wolfe type robust duality between the smooth uncertain optimization problem and its uncertain dual problem by proving the sufficient conditions for a weak duality and a strong duality between the deterministic robust counterpart of the primal model and the optimistic counterpart of its dual problem. The results on robust duality theorems are established in terms of underestimators. Additionally, to illustrate or support this study, some examples are presented.","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80628792","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 modified version of a Benson-type algorithm proposed for obtaining solutions with better dispersion on the non-dominated set of a non-convex multi-objective programming problem","authors":"A. H. Dehmiry, Maryam Kargarfard","doi":"10.3934/naco.2022039","DOIUrl":"https://doi.org/10.3934/naco.2022039","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89532444","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}
A method of finite uniform approximation of an begin{document}$ N $end{document}-person noncooperative game played with staircase-function strategies is presented. A continuous staircase begin{document}$ N $end{document}-person game is approximated to a staircase begin{document}$ N $end{document}-dimensional-matrix game by sampling the player's pure strategy value set. The set is sampled uniformly so that the resulting staircase begin{document}$ N $end{document}-dimensional-matrix game is hypercubic. An equilibrium of the staircase begin{document}$ N $end{document}-dimensional-matrix game is obtained by stacking the equilibria of the subinterval begin{document}$ N $end{document}-dimensional-matrix games, each defined on a subinterval where the pure strategy value is constant. The stack is an approximate solution to the initial staircase game. The (weak) consistency of the approximate solution is studied by how much the players' payoff and equilibrium strategy change as the sampling density minimally increases. The consistency is equivalent to the approximate solution acceptability. An example of a 4-person noncooperative game is presented to show how the approximation is fulfilled for a case of when every subinterval quadmatrix game has pure strategy equilibria.
A method of finite uniform approximation of an begin{document}$ N $end{document}-person noncooperative game played with staircase-function strategies is presented. A continuous staircase begin{document}$ N $end{document}-person game is approximated to a staircase begin{document}$ N $end{document}-dimensional-matrix game by sampling the player's pure strategy value set. The set is sampled uniformly so that the resulting staircase begin{document}$ N $end{document}-dimensional-matrix game is hypercubic. An equilibrium of the staircase begin{document}$ N $end{document}-dimensional-matrix game is obtained by stacking the equilibria of the subinterval begin{document}$ N $end{document}-dimensional-matrix games, each defined on a subinterval where the pure strategy value is constant. The stack is an approximate solution to the initial staircase game. The (weak) consistency of the approximate solution is studied by how much the players' payoff and equilibrium strategy change as the sampling density minimally increases. The consistency is equivalent to the approximate solution acceptability. An example of a 4-person noncooperative game is presented to show how the approximation is fulfilled for a case of when every subinterval quadmatrix game has pure strategy equilibria.
{"title":"Consistency of equilibrium stacks in finite uniform approximation of a noncooperative game played with staircase-function strategies","authors":"V. Romanuke","doi":"10.3934/naco.2022027","DOIUrl":"https://doi.org/10.3934/naco.2022027","url":null,"abstract":"<p style='text-indent:20px;'>A method of finite uniform approximation of an <inline-formula><tex-math id=\"M1\">begin{document}$ N $end{document}</tex-math></inline-formula>-person noncooperative game played with staircase-function strategies is presented. A continuous staircase <inline-formula><tex-math id=\"M2\">begin{document}$ N $end{document}</tex-math></inline-formula>-person game is approximated to a staircase <inline-formula><tex-math id=\"M3\">begin{document}$ N $end{document}</tex-math></inline-formula>-dimensional-matrix game by sampling the player's pure strategy value set. The set is sampled uniformly so that the resulting staircase <inline-formula><tex-math id=\"M4\">begin{document}$ N $end{document}</tex-math></inline-formula>-dimensional-matrix game is hypercubic. An equilibrium of the staircase <inline-formula><tex-math id=\"M5\">begin{document}$ N $end{document}</tex-math></inline-formula>-dimensional-matrix game is obtained by stacking the equilibria of the subinterval <inline-formula><tex-math id=\"M6\">begin{document}$ N $end{document}</tex-math></inline-formula>-dimensional-matrix games, each defined on a subinterval where the pure strategy value is constant. The stack is an approximate solution to the initial staircase game. The (weak) consistency of the approximate solution is studied by how much the players' payoff and equilibrium strategy change as the sampling density minimally increases. The consistency is equivalent to the approximate solution acceptability. An example of a 4-person noncooperative game is presented to show how the approximation is fulfilled for a case of when every subinterval quadmatrix game has pure strategy equilibria.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75939887","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":"Alternated inertial forward-backward-forward splitting algorithm","authors":"","doi":"10.3934/naco.2022035","DOIUrl":"https://doi.org/10.3934/naco.2022035","url":null,"abstract":"","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83567977","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}
We analyze the method of solving the separable convex continuous quadratic knapsack problem by weighted average from the viewpoint of variable fixing. It is shown that this method, considered as a variant of the variable fixing algorithms, and Kiwiel's variable fixing method generate the same iterates. We further improve the algorithm based on the analysis regarding the semismooth Newton method. Computational results are given and comparisons are made among the state-of-the-art algorithms. Experiments show that our algorithm has significantly good performance; it behaves very much like an begin{document}$ O(n) $end{document} algorithm with a very small constant.
We analyze the method of solving the separable convex continuous quadratic knapsack problem by weighted average from the viewpoint of variable fixing. It is shown that this method, considered as a variant of the variable fixing algorithms, and Kiwiel's variable fixing method generate the same iterates. We further improve the algorithm based on the analysis regarding the semismooth Newton method. Computational results are given and comparisons are made among the state-of-the-art algorithms. Experiments show that our algorithm has significantly good performance; it behaves very much like an begin{document}$ O(n) $end{document} algorithm with a very small constant.
{"title":"Variable fixing method by weighted average for the continuous quadratic knapsack problem","authors":"Hsin-Min Sun, Yu-Juan Sun","doi":"10.3934/naco.2021048","DOIUrl":"https://doi.org/10.3934/naco.2021048","url":null,"abstract":"<p style='text-indent:20px;'>We analyze the method of solving the separable convex continuous quadratic knapsack problem by weighted average from the viewpoint of variable fixing. It is shown that this method, considered as a variant of the variable fixing algorithms, and Kiwiel's variable fixing method generate the same iterates. We further improve the algorithm based on the analysis regarding the semismooth Newton method. Computational results are given and comparisons are made among the state-of-the-art algorithms. Experiments show that our algorithm has significantly good performance; it behaves very much like an <inline-formula><tex-math id=\"M1\">begin{document}$ O(n) $end{document}</tex-math></inline-formula> algorithm with a very small constant.</p>","PeriodicalId":44957,"journal":{"name":"Numerical Algebra Control and Optimization","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80110486","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：