In assessing the quality of poetry,George Santayana advanced a graded criterion that may be termed a“trilevel theory.”Although this conception originally emerged from his reflections on poetry,it came to serve as an...In assessing the quality of poetry,George Santayana advanced a graded criterion that may be termed a“trilevel theory.”Although this conception originally emerged from his reflections on poetry,it came to serve as an overarching framework for his broader literary vision,mirroring his views on some literary elements such as form,matter,and theme.What is especially compelling is the latent unity of Santayana’s diverse intellectual roles—philosopher,aesthetician,and literary critic—within this literary structure.His pursuit of aesthetic excellence,advocacy of realism and literary tradition,philosophical commitment to naturalism and rationalism,and his sense of responsibility as an intellectual are all organically integrated within this idea.展开更多
In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP p...In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP problem into a bilevel programming(BP)problem with complementary constraints.Secondly,taking the complementary constraints as penalties and appending them to the upper-level objective,a penalized BP problem is obtained.Thirdly,for the penalized BP problem,we use K-K-T optimality conditions again and append the corresponding complementary conditions to the upper level as penalties.Then,an overall penalized problem for the LTP problem is formed;we analyze the characteristics of the optimal solutions of the overall penalized problem and propose a penalty function algorithm.The numerical results show that the penalty function approach is feasible and effective.展开更多
基金Key Project of Scientific Research of Hunan Provincial Department of Education"A Study of George Santayana's Literary Thought"(No.23A0092).
文摘In assessing the quality of poetry,George Santayana advanced a graded criterion that may be termed a“trilevel theory.”Although this conception originally emerged from his reflections on poetry,it came to serve as an overarching framework for his broader literary vision,mirroring his views on some literary elements such as form,matter,and theme.What is especially compelling is the latent unity of Santayana’s diverse intellectual roles—philosopher,aesthetician,and literary critic—within this literary structure.His pursuit of aesthetic excellence,advocacy of realism and literary tradition,philosophical commitment to naturalism and rationalism,and his sense of responsibility as an intellectual are all organically integrated within this idea.
基金supported by the National Natural Science Foundation of China(Nos.12271061,11771058)the Outstanding Youth Foundation of Hubei Province of China(No.2019CFA088).
文摘In this paper,we mainly focus on the solving approach for the linear trilevel programming(LTP)problem.Firstly,based on the lower-level problem’s Karush–Kuhn–Tucker(K-K-T)optimality conditions,we transform the LTP problem into a bilevel programming(BP)problem with complementary constraints.Secondly,taking the complementary constraints as penalties and appending them to the upper-level objective,a penalized BP problem is obtained.Thirdly,for the penalized BP problem,we use K-K-T optimality conditions again and append the corresponding complementary conditions to the upper level as penalties.Then,an overall penalized problem for the LTP problem is formed;we analyze the characteristics of the optimal solutions of the overall penalized problem and propose a penalty function algorithm.The numerical results show that the penalty function approach is feasible and effective.
