The conditional quadratic semidefinite programming(cQSDP)refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace,and the objectives are quadratic...The conditional quadratic semidefinite programming(cQSDP)refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace,and the objectives are quadratic.The chief purpose of this paper is to focus on two primal examples of cQSDP:the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem.For the latter problem,we review some classical contributions and establish certain links among them.Moreover,we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy.We also include an application in calibrating the correlation matrix in Libor market models.We hope this work will stimulate new research in cQSDP.展开更多
Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the rela...Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the relations among all these conditions are illustrated by a unified approach;still more, unlike the sufficient conditions previously given in the literature,a new necessary condition is put forward at the end of the paper, so that it implies more applications.展开更多
基金supported by the Engineering and Physical Sciences Research Council Grant(No.EP/K007645/1).
文摘The conditional quadratic semidefinite programming(cQSDP)refers to a class of matrix optimization problems whose matrix variables are required to be positive semidefinite on a subspace,and the objectives are quadratic.The chief purpose of this paper is to focus on two primal examples of cQSDP:the problem of matrix completion/approximation on a subspace and the Euclidean distance matrix problem.For the latter problem,we review some classical contributions and establish certain links among them.Moreover,we develop a semismooth Newton method for a special class of cQSDP and establish its quadratic convergence under the condition of constraint nondegeneracy.We also include an application in calibrating the correlation matrix in Libor market models.We hope this work will stimulate new research in cQSDP.
文摘Since the point-to-set maps were introduced by Zangwill in the study of conceptual algorithms, various sufficient conditions for the algorithms to be of global convergence have been established.In this paper, the relations among all these conditions are illustrated by a unified approach;still more, unlike the sufficient conditions previously given in the literature,a new necessary condition is put forward at the end of the paper, so that it implies more applications.
