Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Ou...Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.展开更多
In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' ...In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.展开更多
In this article, we consider the multiclass network equilibrium problems. A so called strongly valid toll can support any multiclass user equilibrium flow pattern as a system minimum when the system objective function...In this article, we consider the multiclass network equilibrium problems. A so called strongly valid toll can support any multiclass user equilibrium flow pattern as a system minimum when the system objective function is measured by total emission. Using Hoffman lemma and exact penalization method, we provide the existence of strongly valid tolls for multiclass network equilibrium problems.展开更多
In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in ...In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.展开更多
In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of non...In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.展开更多
The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary con...The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.展开更多
Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a m...Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.展开更多
The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solut...The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.展开更多
In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solut...In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solution of the quasi-equilibrium problem.展开更多
The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for ...The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.展开更多
The tectonic characteristics and research problems of five earthquakes with M≥7.0 on the North China Plain over the last 300 years are addressed in the paper, including the cognition that there were no ground fractur...The tectonic characteristics and research problems of five earthquakes with M≥7.0 on the North China Plain over the last 300 years are addressed in the paper, including the cognition that there were no ground fractures in the 1966 Xingtai earthquake, the question caused by the thrust activity of the seismic fault of the Tangshan Earthquake and the discussion of the seismotectonic environment of the 1830 Cixian earthquake and the 1937 Heze earthquake. The author thinks that the main reason for the problems in research of strong earthquake tectonics in the region is that the status of activity of the main tectonics during the Late Quaternary are unknown. This affects the founding of discrimination criteria for seismotectonics of strong earthquakes on the North China Plain. Discriminating the Holocene active faults from the large number of faults is the most effective method for seismic hazard assessment in the area in future.展开更多
Let Ω be a bounded domain with smooth boundary Ω in R~n. We consider the following eigenvalue problem for systems of elliptic equations under the natural growth conditions
The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly ...The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.展开更多
The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converge...The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.展开更多
In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and gener...In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.展开更多
A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set ...A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.展开更多
In this paper, by using the Lagrangian coordinates, the strongly oblique interactions between solitary waves with the same mode in a stratified fluid ape discussed, which includes the shallow fluid case and deep fluid...In this paper, by using the Lagrangian coordinates, the strongly oblique interactions between solitary waves with the same mode in a stratified fluid ape discussed, which includes the shallow fluid case and deep fluid case. It is found that the interactions are described by the KP equation for the shallow fluid case, the two-dimensional intermediate long wave equation (2D-ILW equation) for the deep fluid case and the two-dimensional BO equation (2D-BO equation) for the infinite deep fluid case.展开更多
A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems...A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings展开更多
The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum...The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.展开更多
In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such tha...In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.展开更多
文摘Using the algorithm in this paper, we prove the existence of solutions to the gene-ralized strongly nonlinear quasi-complementarity problems and the convergence of theiterative sequences generated by the algorithm. Our results improve and extend thecorresponding results of Noor and Chang-Huang. Moreover, a more general iterativealgorithm for finding the approximate solution of generalized strongly nonlinear quasi-complementarity problems is also given. It is shown that the approximate solution ob-tained by the iterative scheme converges to the exact solution of this quasi-com-plementarity problem.
文摘In this paper, single machine scheduling problems with variable processing time is discussed according to published instances of management engineering. Processing time of a job is the product of a “coefficient' of the job on position i and a “normal' processing time of the job. The criteria considered is to minimize scheduled length of all jobs. A lemma is proposed and proved. In no deadline constrained condition, the problem belongs to polynomial time algorithm. It is proved by using 3 partition that if the problem is deadline constrained, its complexity is strong NP hard. Finally, a conjuncture is proposed that is to be proved.
基金supported by the National Natural Science Foundation of China NSFC:71071035
文摘In this article, we consider the multiclass network equilibrium problems. A so called strongly valid toll can support any multiclass user equilibrium flow pattern as a system minimum when the system objective function is measured by total emission. Using Hoffman lemma and exact penalization method, we provide the existence of strongly valid tolls for multiclass network equilibrium problems.
文摘In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.
文摘In this paper, we introduce a hybrid iterative method for finding a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive mappings. Furthermore, we show a strong convergence theorem under some mild conditions.
文摘The authors of this article are interested in characterization of efficient solutions for special classes of problems. These classes consider semi-strong E-convexity of involved functions. Sufficient and necessary conditions for a feasible solution to be an efficient or properly efficient solution are obtained.
文摘Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.
文摘The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature.
文摘In this paper,we study an extragradient algorithm for approximating solutions of quasi-equilibrium problems in Banach spaces.We prove strong convergence of the sequence generated by the extragradient method to a solution of the quasi-equilibrium problem.
文摘The stability analysis of the solution mappings for vector equilibrium problems is an important topic in optimization theory and its applications. In this paper, we focus on the continuity of the solution mapping for a parametric generalized strong vector equilibrium problem. By virtue of a nonlinear scalarization technique, a new density result of the solution mapping is obtained. Based on the density result, we give sufficient conditions for the lower semicontinuity and the Hausdorff upper semicontinuity of the solution mapping to the parametric generalized strong vector equilibrium problem. In addition, some examples were given to illustrate that our results improve ones in the literature.
文摘The tectonic characteristics and research problems of five earthquakes with M≥7.0 on the North China Plain over the last 300 years are addressed in the paper, including the cognition that there were no ground fractures in the 1966 Xingtai earthquake, the question caused by the thrust activity of the seismic fault of the Tangshan Earthquake and the discussion of the seismotectonic environment of the 1830 Cixian earthquake and the 1937 Heze earthquake. The author thinks that the main reason for the problems in research of strong earthquake tectonics in the region is that the status of activity of the main tectonics during the Late Quaternary are unknown. This affects the founding of discrimination criteria for seismotectonics of strong earthquakes on the North China Plain. Discriminating the Holocene active faults from the large number of faults is the most effective method for seismic hazard assessment in the area in future.
文摘Let Ω be a bounded domain with smooth boundary Ω in R~n. We consider the following eigenvalue problem for systems of elliptic equations under the natural growth conditions
文摘The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature.
基金Supported by the Scientific Research Fund of Sichuan Provincial Department of Science and Technology(2015JY0165,2011JYZ011)the Scientific Research Fund of Sichuan Provincial Education Department(14ZA0271)+2 种基金the Scientific Research Project of Yibin University(2013YY06)the Natural Science Foundation of China Medical University,Taiwanthe National Natural Science Foundation of China(11361070)
文摘The purpose of this article is to introduce a general split feasibility problems for two families of nonexpansive mappings in Hilbert spaces. We prove that the sequence generated by the proposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.
文摘In this works, by using the modified viscosity approximation method associated with Meir-Keeler contractions, we proved the convergence theorem for solving the fixed point problem of a nonexpansive semigroup and generalized mixed equilibrium problems in Hilbert spaces.
基金supported by the National Natural Science Foundation of China (No.11071169)supported by the Research Project of Shaoxing University(No.09LG1002)
文摘A new hybrid projection iterative scheme is introduced to approximate a common element of the solution set of a generalized mixed equilibrium problem, the solution set of a variational inequality problem, and the set of fixed points of a relatively weak nonexpansive mapping in the Banach spaces. The obtained results generalize and improve the recent results announced by many other authors.
文摘In this paper, by using the Lagrangian coordinates, the strongly oblique interactions between solitary waves with the same mode in a stratified fluid ape discussed, which includes the shallow fluid case and deep fluid case. It is found that the interactions are described by the KP equation for the shallow fluid case, the two-dimensional intermediate long wave equation (2D-ILW equation) for the deep fluid case and the two-dimensional BO equation (2D-BO equation) for the infinite deep fluid case.
基金Project supported by the Natural Science Foundation of Sichuan Educational Commission (No.2003A081)
文摘A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings
文摘The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.
基金Supported by National Natural Science Foundation of China(79790 1 30 ) and National863Hi- TechProject(863- 30 6- ZT0 4 - 0 4 -
文摘In this paper,a new model for inverse network flow problems,robust partial inverse problem is presented. For a given partial solution,the robust partial inverse problem is to modify the coefficients optimally such that all full solutions containing the partial solution become optimal under new coefficients. It has been shown that the robust partial inverse spanning tree problem can be formulated as a combinatorial linear program,while the robust partial inverse minimum cut problem and the robust partial inverse assignment problem can be solved by combinatorial strongly polynomial algorithms.
