Pub Date : 2023-09-13DOI: 10.1007/s40314-023-02446-z
Max L. N. Gonçalves, Tiago C. Menezes
{"title":"A framework for convex-constrained monotone nonlinear equations and its special cases","authors":"Max L. N. Gonçalves, Tiago C. Menezes","doi":"10.1007/s40314-023-02446-z","DOIUrl":"https://doi.org/10.1007/s40314-023-02446-z","url":null,"abstract":"","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"361 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135740815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-11DOI: 10.1007/s40314-023-02441-4
Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen
{"title":"Inertial proximal point algorithm for the split common solution problem of monotone operator equations","authors":"Nguyen Song Ha, Truong Minh Tuyen, Phan Thi Van Huyen","doi":"10.1007/s40314-023-02441-4","DOIUrl":"https://doi.org/10.1007/s40314-023-02441-4","url":null,"abstract":"","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135982015","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-11DOI: 10.1007/s40314-023-02437-0
Nina Chiarelli, Matjaž Krnc, Martin Milanič, Ulrich Pferschy, Joachim Schauer
Abstract We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent incompatible pairs of items which should not be allocated to the same agent. This setting combines the issues of P artition and I ndependent S et and can be seen as a partial coloring of the conflict graph. In the resulting optimization problem, each agent has its own valuation function for the profits of the items. We aim at maximizing the lowest total profit obtained by any of the agents. In a previous paper, this problem was shown to be strongly -hard for several well-known graph classes, e.g., bipartite graphs and their line graphs. On the other hand, it was shown that pseudo-polynomial time algorithms exist for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. In this contribution, we extend this line of research by developing pseudo-polynomial time algorithms that solve the problem for the class of convex bipartite conflict graphs, graphs of bounded clique-width, and graphs of bounded tree-independence number. The algorithms are based on dynamic programming and also permit fully polynomial-time approximation schemes (FPTAS).
{"title":"Fair allocation algorithms for indivisible items under structured conflict constraints","authors":"Nina Chiarelli, Matjaž Krnc, Martin Milanič, Ulrich Pferschy, Joachim Schauer","doi":"10.1007/s40314-023-02437-0","DOIUrl":"https://doi.org/10.1007/s40314-023-02437-0","url":null,"abstract":"Abstract We consider the fair allocation of indivisible items to several agents with additional conflict constraints. These are represented by a conflict graph where each item corresponds to a vertex of the graph and edges in the graph represent incompatible pairs of items which should not be allocated to the same agent. This setting combines the issues of P artition and I ndependent S et and can be seen as a partial coloring of the conflict graph. In the resulting optimization problem, each agent has its own valuation function for the profits of the items. We aim at maximizing the lowest total profit obtained by any of the agents. In a previous paper, this problem was shown to be strongly -hard for several well-known graph classes, e.g., bipartite graphs and their line graphs. On the other hand, it was shown that pseudo-polynomial time algorithms exist for the classes of chordal graphs, cocomparability graphs, biconvex bipartite graphs, and graphs of bounded treewidth. In this contribution, we extend this line of research by developing pseudo-polynomial time algorithms that solve the problem for the class of convex bipartite conflict graphs, graphs of bounded clique-width, and graphs of bounded tree-independence number. The algorithms are based on dynamic programming and also permit fully polynomial-time approximation schemes (FPTAS).","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135981696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-01DOI: 10.1007/s40314-023-02439-y
Gang Ren, Guanglan Gao
{"title":"Retraction Note to: A fast adaptive algorithm for nonlinear inverse problems with convex penalty","authors":"Gang Ren, Guanglan Gao","doi":"10.1007/s40314-023-02439-y","DOIUrl":"https://doi.org/10.1007/s40314-023-02439-y","url":null,"abstract":"","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135049686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300004
V. Ruas
An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.
{"title":"A weighted mass explicit scheme for convection-diffusion equations","authors":"V. Ruas","doi":"10.1590/S1807-03022012000300004","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300004","url":null,"abstract":"An explicit scheme based on a weighted mass matrix, for solving time-dependent convection-diffusion problems was recently proposed by the author and collaborators. Convenient bounds for the time step, in terms of both the method's weights and the mesh step size, ensure its stability in space and time, for piecewise linear finite element discretisations in any space dimension. In this work we study some techniques for choosing the weights that guarantee the convergence of the scheme with optimal order in the space-time maximum norm, as both discretisation parameters tend to zero. Mathematical subject classification: Primary: 65M60; Secondary: 76Rxx.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"57 1","pages":"505-522"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85881823","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300006
J. R. Arballo, L. Campañone, R. Mascheroni
The mass and energy transfer during osmotic microwave drying (OD-MWD) process was studied theoretically by modeling and numerical simulation. With the aim to describe the transport phenomena that occurs during the combined dehydration process, the mass and energy microscopic balances were solved. An osmotic-diffusional model was used for osmotic dehydration (OD). On the other hand, the microwave drying (MWD) was modeled solving the mass and heat balances, using properties as function of temperature, moisture and soluble solids content. The obtained balances form highly coupled non-linear differential equations that were solved applying numerical methods. For osmotic dehydration, the mass balances formed coupled ordinary differential equations that were solved using the Fourth-order Runge Kutta method. In the case of microwave drying, the balances constituted partial differential equations, which were solved through Crank-Nicolson implicit finite differences method. The numerical methods were coded in Matlab 7.2 (Mathworks, Natick, MA). The developed mathematical model allows predict the temperature and moisture evolution through the combined dehydration process. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.
{"title":"Numerical solution of coupled mass and energy balances during osmotic microwave dehydration","authors":"J. R. Arballo, L. Campañone, R. Mascheroni","doi":"10.1590/S1807-03022012000300006","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300006","url":null,"abstract":"The mass and energy transfer during osmotic microwave drying (OD-MWD) process was studied theoretically by modeling and numerical simulation. With the aim to describe the transport phenomena that occurs during the combined dehydration process, the mass and energy microscopic balances were solved. An osmotic-diffusional model was used for osmotic dehydration (OD). On the other hand, the microwave drying (MWD) was modeled solving the mass and heat balances, using properties as function of temperature, moisture and soluble solids content. The obtained balances form highly coupled non-linear differential equations that were solved applying numerical methods. For osmotic dehydration, the mass balances formed coupled ordinary differential equations that were solved using the Fourth-order Runge Kutta method. In the case of microwave drying, the balances constituted partial differential equations, which were solved through Crank-Nicolson implicit finite differences method. The numerical methods were coded in Matlab 7.2 (Mathworks, Natick, MA). The developed mathematical model allows predict the temperature and moisture evolution through the combined dehydration process. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"7 1","pages":"539-558"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82370693","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300003
I. P. Santos, R. C. Almeida, S. Malta
This paper presents the numerical analysis of the Nonlinear Subgrid Scale (NSGS) model for approximating singularly perturbed transport models. The NSGS is a free parameter subgrid stabilizing method that introduces an extra stability only onto the subgrid scales. Thisnew feature comes from the local control yielded by decomposing the velocity field into the resolved and unresolved scales. Such decomposition is determined by requiring the minimum of the kinetic energy associated to the unresolved scales and the satisfaction of the resolved scale model problem at element level. The developed method is robust for a wide scope of singularly perturbed problems. Here, we establish the existence and uniqueness of the solution, and provide an a priori error estimate. Convergence tests on two-dimensional examples are reported. Mathematical subject classification: Primary: 65N12; Secondary: 74S05.
{"title":"Numerical analysis of the nonlinear subgrid scale method","authors":"I. P. Santos, R. C. Almeida, S. Malta","doi":"10.1590/S1807-03022012000300003","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300003","url":null,"abstract":"This paper presents the numerical analysis of the Nonlinear Subgrid Scale (NSGS) model for approximating singularly perturbed transport models. The NSGS is a free parameter subgrid stabilizing method that introduces an extra stability only onto the subgrid scales. Thisnew feature comes from the local control yielded by decomposing the velocity field into the resolved and unresolved scales. Such decomposition is determined by requiring the minimum of the kinetic energy associated to the unresolved scales and the satisfaction of the resolved scale model problem at element level. The developed method is robust for a wide scope of singularly perturbed problems. Here, we establish the existence and uniqueness of the solution, and provide an a priori error estimate. Convergence tests on two-dimensional examples are reported. Mathematical subject classification: Primary: 65N12; Secondary: 74S05.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"13 1","pages":"473-503"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87961742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2012-12-06DOI: 10.1590/S1807-03022012000300008
W. Lodwick
Two new powerful mathematical languages, fuzzy set theory and possibility theory, have led to two optimization types that explicitly incorporate data whose values are not real-valued nor probabilistic: 1) flexible optimization and 2) optimization under generalized uncertainty. Our aim is to make clear what these two types are, make distinctions, and show how they can be applied. Flexible optimization arises when it is necessary to relax the meaning of the mathematical relation of belonging to a set (a constraint set in the context of optimization). The mathematical language of relaxed set belonging is fuzzy set theory. Optimization under generalized uncertainty arises when it is necessary to represent parameters of a model whose values are only known partially or incompletely. A natural mathematical language for the representation of partial or incomplete information about the value of a parameter is possibility theory. Flexible optimization, as delineated here, includes much of what has been called fuzzy optimization whereas optimization under generalized uncertainty includes what has been called possibilistic optimization. We explore why flexible optimization and optimization under generalized uncertainty are distinct and important types of optimization problems. Possibility theory in the context of optimization leads to two distinct types of optimization under generalized uncertainty, single distribution and dual distribution optimization. Dual (possibility/necessity pairs) distribution optimization is new. Mathematical subject classification: 90C70, 65G40.
{"title":"An overview of flexibility and generalized uncertainty in optimization","authors":"W. Lodwick","doi":"10.1590/S1807-03022012000300008","DOIUrl":"https://doi.org/10.1590/S1807-03022012000300008","url":null,"abstract":"Two new powerful mathematical languages, fuzzy set theory and possibility theory, have led to two optimization types that explicitly incorporate data whose values are not real-valued nor probabilistic: 1) flexible optimization and 2) optimization under generalized uncertainty. Our aim is to make clear what these two types are, make distinctions, and show how they can be applied. Flexible optimization arises when it is necessary to relax the meaning of the mathematical relation of belonging to a set (a constraint set in the context of optimization). The mathematical language of relaxed set belonging is fuzzy set theory. Optimization under generalized uncertainty arises when it is necessary to represent parameters of a model whose values are only known partially or incompletely. A natural mathematical language for the representation of partial or incomplete information about the value of a parameter is possibility theory. Flexible optimization, as delineated here, includes much of what has been called fuzzy optimization whereas optimization under generalized uncertainty includes what has been called possibilistic optimization. We explore why flexible optimization and optimization under generalized uncertainty are distinct and important types of optimization problems. Possibility theory in the context of optimization leads to two distinct types of optimization under generalized uncertainty, single distribution and dual distribution optimization. Dual (possibility/necessity pairs) distribution optimization is new. Mathematical subject classification: 90C70, 65G40.","PeriodicalId":50649,"journal":{"name":"Computational & Applied Mathematics","volume":"15 1","pages":"569-589"},"PeriodicalIF":2.6,"publicationDate":"2012-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78449527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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