In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various...In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.展开更多
In order to provide scientists with a computational methodology and some computational tools to program their epistemic processes in scientific discovery, we are establishing a novel programming paradigm, named ‘Epis...In order to provide scientists with a computational methodology and some computational tools to program their epistemic processes in scientific discovery, we are establishing a novel programming paradigm, named ‘Epistemic Programming’, which regards conditionals as the subject of computing, takes primary epistemic operations as basic operations of computing, and regards epistemic processes as the subject of programming. This paper presents our fundamental observations and assumptions on scientific discovery processes and their automation, research problems on modeling, automating, and programming epistemic processes, and an outline of our research project of Epistemic Programming.展开更多
This study discusses a guideline on a proper use of Data Envelopment Analysis (DEA) that has been widely used for performance analysis in public and private sectors. The use of DEA is equipped with Strong Complementar...This study discusses a guideline on a proper use of Data Envelopment Analysis (DEA) that has been widely used for performance analysis in public and private sectors. The use of DEA is equipped with Strong Complementary Slackness Conditions (SCSCs) in this study, but an application of DEA/SCSCs depends upon its careful use, as summarized in the guideline. The guideline consists of the five suggestions. First, a data set used in the DEA applications should not have a ratio variable (e.g., financial ratios) in an input(s) and/or an output(s). Second, radial DEA models under variable and constant Returns to Scale (RTS) need a special treatment on zero in a data set. Third, the DEA evaluation needs to drop an outlier. Fourth, an imprecise number (e.g., 1/3) may suffer from a round-off error because DEA needs to specify it in a precise expression to operate a computer code. Finally, when a large input or output variable may dominate other variables in DEA computation, it is necessary to normalize the data set or simply to divide each observation by its average. Such a simple treatment produces more reliable DEA results than the one without any data adjustment. This study also discusses how to handle an occurrence of zero in DEA multipliers by applying SCSCs. The DEA/SCSCs can serve for a multiplier restriction approach without any prior information. Thus, the propesed DEA/SCSCs can provide more reliable results than a straight use of DEA.展开更多
this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al....this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.展开更多
基金Supported by the Natural Science Foundation of Zhejiang Province(LY21A010021)the National Natural Science Foundation of China(11701506)。
文摘In this paper,we investigate three canonical forms of interval convex quadratic pro-gramming problems.Necessary and suficient conditions for checking weak and strong optimality of given vector corresponding to various forms of feasible region,are established respectively.By using the concept of feasible direction,these conditions are formulated in the form of linear systems with both equations and inequalities.In addition,we provide two specific examples to illustrate the efficiency of the conditions.
基金Supported in part by The Ministry of EducationCulture+1 种基金SportsScience and Technology of Japan under Grant-in-Aid for Explor
文摘In order to provide scientists with a computational methodology and some computational tools to program their epistemic processes in scientific discovery, we are establishing a novel programming paradigm, named ‘Epistemic Programming’, which regards conditionals as the subject of computing, takes primary epistemic operations as basic operations of computing, and regards epistemic processes as the subject of programming. This paper presents our fundamental observations and assumptions on scientific discovery processes and their automation, research problems on modeling, automating, and programming epistemic processes, and an outline of our research project of Epistemic Programming.
文摘This study discusses a guideline on a proper use of Data Envelopment Analysis (DEA) that has been widely used for performance analysis in public and private sectors. The use of DEA is equipped with Strong Complementary Slackness Conditions (SCSCs) in this study, but an application of DEA/SCSCs depends upon its careful use, as summarized in the guideline. The guideline consists of the five suggestions. First, a data set used in the DEA applications should not have a ratio variable (e.g., financial ratios) in an input(s) and/or an output(s). Second, radial DEA models under variable and constant Returns to Scale (RTS) need a special treatment on zero in a data set. Third, the DEA evaluation needs to drop an outlier. Fourth, an imprecise number (e.g., 1/3) may suffer from a round-off error because DEA needs to specify it in a precise expression to operate a computer code. Finally, when a large input or output variable may dominate other variables in DEA computation, it is necessary to normalize the data set or simply to divide each observation by its average. Such a simple treatment produces more reliable DEA results than the one without any data adjustment. This study also discusses how to handle an occurrence of zero in DEA multipliers by applying SCSCs. The DEA/SCSCs can serve for a multiplier restriction approach without any prior information. Thus, the propesed DEA/SCSCs can provide more reliable results than a straight use of DEA.
基金Supported in part by NSFC(No.11961011)Guangxi Science and Technology Base and Talents Special Project(No.2021AC06001).
文摘this paper,we propose a class of smoothing-regularization methods for solving the mathematical programming with vanishing constraints.These methods include the smoothing-regularization method proposed by Kanzow et al.in[Comput.Optim.Appl.,2013,55(3):733-767]as a special case.Under the weaker conditions than the ones that have been used by Kanzow et al.in 2013,we prove that the Mangasarian-Fromovitz constraint qualification holds at the feasible points of smoothing-regularization problem.We also analyze that the convergence behavior of the proposed smoothing-regularization method under mild conditions,i.e.,any accumulation point of the stationary point sequence for the smoothing-regularization problem is a strong stationary point.Finally,numerical experiments are given to show the efficiency of the proposed methods.
