In this paper, we provide a complete characterization of the robust isolated calmness of the Karush-Kuhn-Tucker （KKT） solution mapping for convex constrained optimization problems regularized by the nuclear norm fun...In this paper, we provide a complete characterization of the robust isolated calmness of the Karush-Kuhn-Tucker （KKT） solution mapping for convex constrained optimization problems regularized by the nuclear norm function. This study is motivated by the recent work in [8], where the authors show that under the Robinson constraint qualification at a local optimal solution, the KKT solution mapping for a wide class of conic programming problems is robustly isolated calm if and only if both the second order sufficient condition （SOSC） and the strict Robinson constraint qualification （SRCQ） are satisfied. Based on the variational properties of the nuclear norm function and its conjugate, we establish the equivalence between the primal/dual SOSC and the dual/primal SRCQ. The derived results lead to several equivalent characterizations of the robust isolated calmness of the KKT solution mapping and add insights to the existing literature on the stability of nuclear norm regularized convex optimization problems.展开更多
1 Authorities in Montgomery Township,Pennsylvania,have introduced wavy lane patterns on some streets in an effort to slow down traffic in the area.2 Driving along Grays Lane in Montgomery Township for the first time m...1 Authorities in Montgomery Township,Pennsylvania,have introduced wavy lane patterns on some streets in an effort to slow down traffic in the area.2 Driving along Grays Lane in Montgomery Township for the first time must be challenging.Thats because the regular lane patterns have been replaced by wavy and zig⁃zag lines that look like they were painted by a drunk.But they are wavy by design.According to Montgomery Township officials,the unusual patterns were thought as the best solution to discouraging speeding on some of the streets.Police sources told local media outlets that the“traffic⁃calming measures”were installed in response to numerous complaints about certain streets being used as“speedways”.展开更多
Earthquake,tsunami,nuclear plantb reakdown.Each is a major catast rophe.But Japan has been hit by all of them.Homelessness,economic losses,release of radiation.Each is a huge challenge.Now Japan must face all three.Ho...Earthquake,tsunami,nuclear plantb reakdown.Each is a major catast rophe.But Japan has been hit by all of them.Homelessness,economic losses,release of radiation.Each is a huge challenge.Now Japan must face all three.How will Japan respond to the domino-like disaster展开更多
文摘In this paper, we provide a complete characterization of the robust isolated calmness of the Karush-Kuhn-Tucker （KKT） solution mapping for convex constrained optimization problems regularized by the nuclear norm function. This study is motivated by the recent work in [8], where the authors show that under the Robinson constraint qualification at a local optimal solution, the KKT solution mapping for a wide class of conic programming problems is robustly isolated calm if and only if both the second order sufficient condition （SOSC） and the strict Robinson constraint qualification （SRCQ） are satisfied. Based on the variational properties of the nuclear norm function and its conjugate, we establish the equivalence between the primal/dual SOSC and the dual/primal SRCQ. The derived results lead to several equivalent characterizations of the robust isolated calmness of the KKT solution mapping and add insights to the existing literature on the stability of nuclear norm regularized convex optimization problems.
文摘1 Authorities in Montgomery Township,Pennsylvania,have introduced wavy lane patterns on some streets in an effort to slow down traffic in the area.2 Driving along Grays Lane in Montgomery Township for the first time must be challenging.Thats because the regular lane patterns have been replaced by wavy and zig⁃zag lines that look like they were painted by a drunk.But they are wavy by design.According to Montgomery Township officials,the unusual patterns were thought as the best solution to discouraging speeding on some of the streets.Police sources told local media outlets that the“traffic⁃calming measures”were installed in response to numerous complaints about certain streets being used as“speedways”.
文摘Earthquake,tsunami,nuclear plantb reakdown.Each is a major catast rophe.But Japan has been hit by all of them.Homelessness,economic losses,release of radiation.Each is a huge challenge.Now Japan must face all three.How will Japan respond to the domino-like disaster
文摘为阐明鹅Calm1基因结构特征及其表达规律。克隆四川白鹅Calm1基因编码区序列并进行生物信息学分析,应用实时荧光定量PCR技术检测鹅不同等级卵泡和不同组织中Calm1基因的相对表达量。鹅Calm1基因编码区序列全长为450 bp,编码149个氨基酸,其氨基酸序列与原鸡相似性为99%。鹅大脑中Calm1表达量显著高于其他组织(P<0.05)。Calm1在不同等级卵泡组织中均有表达,F2级卵泡中Calm1表达量是小白卵泡(Small white follicles,SWF)的1.76倍(P<0.05),且显著高于F5、F4、F3和F1级卵泡(P<0.05);在排卵后卵泡(Postovulatory follicle,POF)组织中,POF1级卵泡组织中Calm1表达量显著高于POF2、POF3和POF4级卵泡(P<0.05);卵巢组织中Calm1的表达量,是小白卵泡的1.75倍(P<0.05)。Calm1是高度保守、广泛表达的蛋白质,Calm1可能通过影响卵泡细胞增殖和类固醇激素合成来参与调控动物繁殖。
