Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used ...Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used as the initial value of the chaotic system. Second, the chaotic sequence and Fisher–Yatess scrambling are used to scramble the plaintext,and a sorting scrambling algorithm is used for secondary scrambling. Then, the chaotic sequence and DNA coding rules are used to change the plaintext pixel values, which makes the ciphertext more random and resistant to attacks, and thus ensures that the encrypted ciphertext is more secure. Finally, we add plaintext statistics for pixel-level diffusion to ensure plaintext sensitivity. The experimental results and security analysis show that the new algorithm has a good encryption effect and speed, and can also resist common attacks.展开更多
This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div|u|p-2um)+|x|α uq ,(x,t)∈RN×(0,t),where N ≥ 1, 1 〈 p 〈 2, m 〉 max(0,3 -p/N} satisfyi...This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div|u|p-2um)+|x|α uq ,(x,t)∈RN×(0,t),where N ≥ 1, 1 〈 p 〈 2, m 〉 max(0,3 -p/N} satisfying 2 〈 p+m 〈 3, q 〉 1, and(α 〉 N(3 - p - m) - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.展开更多
For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtai...For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtain the complete convergence rates. Our results extend some known ones.展开更多
We first prove various kinds of expressions for modulus of random convexity by using an L^0(F, R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random...We first prove various kinds of expressions for modulus of random convexity by using an L^0(F, R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0(F, X) derived from a normed space X by the classical modulus of convexity of X.展开更多
Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we ...Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.展开更多
In this paper,nonsmooth univex,nonsmooth quasiunivex,and nonsmooth pseudounivex functions are introduced.By utilizing these new concepts,sufficient optimality conditions for a weakly efficient solution of the nonsmoot...In this paper,nonsmooth univex,nonsmooth quasiunivex,and nonsmooth pseudounivex functions are introduced.By utilizing these new concepts,sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established.Weak and strong duality theorems are also derived for Mond-Weir type multiobjective dual programs.展开更多
This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled sys...This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.展开更多
This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived fi...This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.展开更多
This paper studies the problem of isochronal synchronization of chaotic systems with time-delayed mutual coupling. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed f...This paper studies the problem of isochronal synchronization of chaotic systems with time-delayed mutual coupling. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed for the stability of isochronal synchronization between two identical chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to isochronally synchronize two identical chaotic systems with delay-coupled, so this scheme is analytical, and simple to implement in practice. Simulation results show that the isochronal synchronization behavior is determined by time delay.展开更多
Let(Ω,E,P)be a probability space,F a sub-σ-algebra of E,Lp(E)(1 p+∞)the classical function space and Lp F(E)the L0(F)-module generated by Lp(E),which can be made into a random normed module in a natural way.Up to t...Let(Ω,E,P)be a probability space,F a sub-σ-algebra of E,Lp(E)(1 p+∞)the classical function space and Lp F(E)the L0(F)-module generated by Lp(E),which can be made into a random normed module in a natural way.Up to the present time,there are three kinds of conditional risk measures,whose model spaces are L∞(E),Lp(E)(1 p<+∞)and Lp F(E)(1 p+∞)respectively,and a conditional convex dual representation theorem has been established for each kind.The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems.We first establish the relation between Lp(E)and Lp F(E),namely Lp F(E)=Hcc(Lp(E)),which shows that Lp F(E)is exactly the countable concatenation hull of Lp(E).Based on the precise relation,we then prove that every L0(F)-convex Lp(E)-conditional risk measure(1 p+∞)can be uniquely extended to an L0(F)-convex Lp F(E)-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter,which shows that the study of Lp-conditional risk measures can be incorporated into that of Lp F(E)-conditional risk measures.In particular,in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L0-convex conditional risk measures.展开更多
Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected ...Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.展开更多
In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasico...In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasiconvex functions are introduced,respectively.By utilizing these new concepts,sufficient optimality conditions of approximate solutions for the nonsmooth semi-infinite programming problem are established.Some examples are also presented.The results obtained in this paper improve the corresponding results of Son et al.(J Optim Theory Appl 141:389–409,2009).展开更多
One of the most interesting problems of nonlinear differential equations is the construction of partial solutions. A new method is presented in this paper to seek special solutions of nonlinear diffusion equations. Th...One of the most interesting problems of nonlinear differential equations is the construction of partial solutions. A new method is presented in this paper to seek special solutions of nonlinear diffusion equations. This method is based on seeking suitable function to satisfy Bernolli equation. Many new special solutions are obtained.展开更多
Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a s...Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard X2-1imit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.展开更多
We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are establishe...We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.展开更多
The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessaril...The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.展开更多
This paper proposes a new approach for variable selection in partially linear errors-in-variables (EV) models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simult...This paper proposes a new approach for variable selection in partially linear errors-in-variables (EV) models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61173183,61672124,61370145,and 11501064)the Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund,China(Grant No.MMJJ20170203)+1 种基金the China Postdoctoral Science Foundation(Grant No.2016M590850)the Scientific and Technological Research Program of Chongqing Municipal Education Commission,China(Grant No.KJ1500605)
文摘Based on the Fisher–Yatess scrambling and DNA coding technology, a chaotical image encryption method is proposed. First, the SHA-3 algorithm is used to calculate the hash value of the initial password, which is used as the initial value of the chaotic system. Second, the chaotic sequence and Fisher–Yatess scrambling are used to scramble the plaintext,and a sorting scrambling algorithm is used for secondary scrambling. Then, the chaotic sequence and DNA coding rules are used to change the plaintext pixel values, which makes the ciphertext more random and resistant to attacks, and thus ensures that the encrypted ciphertext is more secure. Finally, we add plaintext statistics for pixel-level diffusion to ensure plaintext sensitivity. The experimental results and security analysis show that the new algorithm has a good encryption effect and speed, and can also resist common attacks.
基金partially supported by the Doctor Start-up Funding and Natural Science Foundation of Chongqing University of Posts and Telecommunications(A2014-25 and A2014-106)partially supported by Scientific and Technological Research Program of Chongqing Municipal Education Commission(KJ1500403)+3 种基金the Basic and Advanced Research Project of CQCSTC(cstc2015jcyj A00008)partially supported by NSFC(11371384),partially supported by NSFC(11426047)the Basic and Advanced Research Project of CQCSTC(cstc2014jcyj A00040)the Research Fund of Chongqing Technology and Business University(2014-56-11)
文摘This paper deals with the Cauchy problem for a doubly singular parabolic equation with a weighted source ut=div|u|p-2um)+|x|α uq ,(x,t)∈RN×(0,t),where N ≥ 1, 1 〈 p 〈 2, m 〉 max(0,3 -p/N} satisfying 2 〈 p+m 〈 3, q 〉 1, and(α 〉 N(3 - p - m) - p. We give the secondary critical exponent on the decay asymptotic behavior of an initial value at infinity for the existence and non-existence of global solutions of the Cauchy problem. Moreover, the life span of solutions is also studied.
文摘For weighted sums of asymptotically almost negatively associated (AANA) random variables sequences, we use the Rosenthal type moment inequalities and prove the Marcinkiewicz-Zygmund type complete convergence and obtain the complete convergence rates. Our results extend some known ones.
基金Supported by National Natural Science Foundation of China(Grant No.11171015)Science Foundation of Chongqing Education Board(Grant No.KJ120732)
文摘We first prove various kinds of expressions for modulus of random convexity by using an L^0(F, R)-valued function's intermediate value theorem and the well known Hahn-Banach theorem for almost surely bounded random linear functionals, then establish some basic properties including continuity for modulus of random convexity. In particular, we express the modulus of random convexity of a special random normed module L^0(F, X) derived from a normed space X by the classical modulus of convexity of X.
基金Supported by National Natural Science Foundation of China (Grant No. 10871016)
文摘Let (Ω, F, P) be a probability space and L0(F,R) the algebra of equivalence classes of real- valued random variables on (Ω, F, P). When L0(F,R) is endowed with the topology of convergence in probability, we prove an intermediate value theorem for a continuous local function from L0(F, R) to L0(F,R). As applications of this theorem, we first give several useful expressions for modulus of random convexity, then we prove that a complete random normed module (S, ||·||) is random uniformly convex iff LP(S) is uniformly convex for each fixed positive number p such that 1 〈 p 〈 +∞.
基金supported by the National Natural Science Foundation of China under Grant No.11001287the Natural Science Foundation Project of Chongqing(CSTC 2010BB9254)the Education Committee Project Research Foundation of Chongqing under Grant No.KJ100711
文摘In this paper,nonsmooth univex,nonsmooth quasiunivex,and nonsmooth pseudounivex functions are introduced.By utilizing these new concepts,sufficient optimality conditions for a weakly efficient solution of the nonsmooth multiobjective programming problem are established.Weak and strong duality theorems are also derived for Mond-Weir type multiobjective dual programs.
基金This research is supported by the National Social Science Foundation of China under Grant No. 11CTJ004, the National Natural Science Foundation of China under Grant Nos. 10871013 and 10871217, the National Natural Science Foundation of Beijing under Grant No. 1102008, the Research Foundation of Chongqing Municipal Education Commission under Grant Nos. KJ110720 and KJ100726, and the Natural Science Foundation of Guangxi under Grant No. 2010GXNSFB013051.
基金supported by the Natural Science Foundation of Chongqing Municipal Education Commission(KJ1706167)and the Program for the introduction of High-Level Talents(1756006,1752003).
文摘This article is devoted to the identification, from observations or field measurements, of the hydraulic conductivity K for the saltwater intrusion problem in confined aquifers. The involved PDE model is a coupled system of nonlinear parabolic-elliptic equations completed by boundary and initial conditions. The main unknowns are the saltwater/freshwater interface depth and the freshwater hydraulic head. The inverse problem is formulated as an optimization problem where the cost function is a least square functional measuring the discrepancy between experimental data and those provided by the model.Considering the exact problem as a constraint for the optimization problem and introducing the Lagrangian associated with the cost function, we prove that the optimality system has at least one solution. Moreover, the first order necessary optimality conditions are established for this optimization problem.
基金supported by the National Natural Science Foundation of China(Nos.11101069,11171237,11471059,and 81171411)the China Postdoctoral Science Foundation(Nos.2014M552328 and2015T80967)the Scientific Research Foundation for the Returned Overseas Chinese Scholars,State Education Ministry
文摘This paper studies the Browder-Tikhonov regularization of a second-order evolution hemivariational inequality (SOEHVI) with non-coercive operators. With duality mapping, the regularized formulations and a derived first-order evolution hemivariational inequality (FOEHVI) for the problem considered are presented. By applying the Browder-Tikhonov regularization method to the derived FOEHVI, a sequence of regularized solutions to the regularized SOEHVI is constructed, and the strong convergence of the whole sequence of regularized solutions to a solution to the problem is proved.
文摘This paper studies the problem of isochronal synchronization of chaotic systems with time-delayed mutual coupling. Based on the invariance principle of differential equations, an adaptive feedback scheme is proposed for the stability of isochronal synchronization between two identical chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically adapted to isochronally synchronize two identical chaotic systems with delay-coupled, so this scheme is analytical, and simple to implement in practice. Simulation results show that the isochronal synchronization behavior is determined by time delay.
基金supported by National Natural Science Foundation of China(Grant Nos.11171015 and 11301568)
文摘Let(Ω,E,P)be a probability space,F a sub-σ-algebra of E,Lp(E)(1 p+∞)the classical function space and Lp F(E)the L0(F)-module generated by Lp(E),which can be made into a random normed module in a natural way.Up to the present time,there are three kinds of conditional risk measures,whose model spaces are L∞(E),Lp(E)(1 p<+∞)and Lp F(E)(1 p+∞)respectively,and a conditional convex dual representation theorem has been established for each kind.The purpose of this paper is to study the relations among the three kinds of conditional risk measures together with their representation theorems.We first establish the relation between Lp(E)and Lp F(E),namely Lp F(E)=Hcc(Lp(E)),which shows that Lp F(E)is exactly the countable concatenation hull of Lp(E).Based on the precise relation,we then prove that every L0(F)-convex Lp(E)-conditional risk measure(1 p+∞)can be uniquely extended to an L0(F)-convex Lp F(E)-conditional risk measure and that the dual representation theorem of the former can also be regarded as a special case of that of the latter,which shows that the study of Lp-conditional risk measures can be incorporated into that of Lp F(E)-conditional risk measures.In particular,in the process we find that combining the countable concatenation hull of a set and the local property of conditional risk measures is a very useful analytic skill that may considerably simplify and improve the study of L0-convex conditional risk measures.
基金supported by National Natural Science Foundation of China(Grant Nos.11301569,11471029 and 11101014)the Beijing Natural Science Foundation(Grant No.1142002)+2 种基金the Science and Technology Project of Beijing Municipal Education Commission(Grant No.KM201410005010)Hong Kong Research Grant(Grant No.HKBU202711)Hong Kong Baptist University FRG Grants(Grant Nos.FRG2/11-12/110 and FRG1/13-14/018)
文摘Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.
基金This work was partially supported by the National Natural Science Foundation of China(Nos.11471059 and 11671282)the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001 and cstc2014jcyjA00033)+2 种基金the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1400630)the Program for University Innovation Team of Chongqing(No.CXTDX201601026)the Education Committee Project Foundation of Bayu Scholar.
文摘In this paper,we study optimality conditions of approximate solutions for nonsmooth semi-infinite programming problems.Three new classes of functions,namelyε-pseudoconvex functions of type I and type II andε-quasiconvex functions are introduced,respectively.By utilizing these new concepts,sufficient optimality conditions of approximate solutions for the nonsmooth semi-infinite programming problem are established.Some examples are also presented.The results obtained in this paper improve the corresponding results of Son et al.(J Optim Theory Appl 141:389–409,2009).
基金Supported by the Natural Science Foundation Project of Chongqing(CSTC,2014jcyj A00026)Science and Technology Research Project of Chongqing Municipal Education Commission(KJ1400614)
文摘One of the most interesting problems of nonlinear differential equations is the construction of partial solutions. A new method is presented in this paper to seek special solutions of nonlinear diffusion equations. This method is based on seeking suitable function to satisfy Bernolli equation. Many new special solutions are obtained.
基金Supported by National Social Science Foundation of China (Grant No. 11CTJ004)National Natural Science Foundation of China (Grant Nos. 11171012 and 11101452)+3 种基金National Natural Science Foundation of Beijing (Grant No. 1102008)Natural Science Foundation Project of CQ CSTC (Grant No. cstcjjA00014)Research Foundation of Chongqing Municipal Education Commission (Grant No. KJ110720)Natural Science Foundation of Guangxi (Grant No. 2010GXNSFB013051)
文摘Empirical-likelihood-based inference for the parameters in a partially linear single-index model with randomly censored data is investigated. We introduce an estimated empirical likelihood for the parameters using a synthetic data approach and show that its limiting distribution is a mixture of central chi-squared distribution. To attack this difficulty we propose an adjusted empirical likelihood to achieve the standard X2-1imit. Furthermore, since the index is of norm 1, we use this constraint to reduce the dimension of parameters, which increases the accuracy of the confidence regions. A simulation study is carried out to compare its finite-sample properties with the existing method. An application to a real data set is illustrated.
基金supported by National Natural Science Foundation of China (Grant Nos. 11431004, 11271391 and 11201511)the Project of Chongqing Science and Technology Committee (Grant No. cstc2014pt-sy00001)Theoretical Foundation and Application Procedure of Environmental Data Envelopment Analysis Model (Grant No. B-Q22L)
文摘We focus on second order duality for a class of multiobjective programming problem subject to cone constraints. Four types of second order duality models are formulated. Weak and strong duality theorems are established in terms of the generalized convexity, respectively. Converse duality theorems, essential parts of duality theory, are presented under appropriate assumptions. Moreover, some deficiencies in the work of Ahmad and Agarwal(2010) are discussed.
基金the National Natural Science Foundation of China(Nos.11471059,11301571,and 11301570)the Chongqing Research Program of Basic Research and Frontier Technology(Nos.cstc2014jcyjA00037,cstc2015jcyjB00001,cstc2015jcyjA00025,and cstc2015jcyjA00002)+2 种基金the Education Committee Project Research Foundation of Chongqing(Nos.KJ1400618 and KJ1500626)the Postdoctoral Science Foundation of China(Nos.2015M580774 and 2016T90837)the Program for University Innovation Team of Chongqing(CXTDX201601026 and CXTDX201601022).
文摘The purpose of this paper is to study the approximate optimality condition for composite convex optimization problems with a cone-convex system in locally convex spaces,where all functions involved are not necessarily lower semicontinuous.By using the properties of the epigraph of conjugate functions,we introduce a new regularity condition and give its equivalent characterizations.Under this new regularity condition,we derive necessary and sufficient optimality conditions ofε-optimal solutions for the composite convex optimization problem.As applications of our results,we derive approximate optimality conditions to cone-convex optimization problems.Our results extend or cover many known results in the literature.
基金Supported by the National Natural Science Foundation of China (Nos.11126332 and 11101452)the National Social Science Foundation of China (No.11CTJ004)+1 种基金the Natural Science Foundation Project of CQ CSTC(No.cstc2011jjA00014)the Research Foundation of Chongqing Municipal Education Commission (No.KJ110720)
文摘This paper proposes a new approach for variable selection in partially linear errors-in-variables (EV) models for longitudinal data by penalizing appropriate estimating functions. We apply the SCAD penalty to simultaneously select significant variables and estimate unknown parameters. The rate of convergence and the asymptotic normality of the resulting estimators are established. Furthermore, with proper choice of regularization parameters, we show that the proposed estimators perform as well as the oracle procedure. A new algorithm is proposed for solving penalized estimating equation. The asymptotic results are augmented by a simulation study.