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Mio Murao  One of the best experts on this subject based on the ideXlab platform.

adaptive experimental design for one qubit state estimation with finite data based on a statistical update criterion
Physical Review A, 2012CoAuthors: Takanori Sugiyama, Peter S Turner, Mio MuraoAbstract:We consider 1qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the averagevarianceOptimality (AOptimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A optimization is a nonlinear minimization problem; however, we find an analytic solution for 1qubit state estimation using projective measurements, reducing computational effort. We compare numerically the performances of two adaptive and two nonadaptive schemes for finite data sets and show that the AOptimality criterion gives more precise estimates than standard quantum tomography.

adaptive experimental design for one qubit state estimation with finite data based on a statistical update criterion
Physical Review A, 2012CoAuthors: Takanori Sugiyama, Peter S Turner, Mio MuraoAbstract:We consider 1qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the averagevarianceOptimality (AOptimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, Aoptimization is a nonlinear minimization problem; however, we find an analytic solution for 1qubit state estimation using projective measurements, reducing computational effort. We compare numerically two adaptive and two nonadaptive schemes for finite data sets and show that the AOptimality criterion gives more precise estimates than standard quantum tomography.
Kensuke Tanaka  One of the best experts on this subject based on the ideXlab platform.

necessary and sufficient conditions for minimax fractional programming
Journal of Mathematical Analysis and Applications, 1999CoAuthors: Hangchin Lai, J. C. Liu, Kensuke TanakaAbstract:We establish the necessary and sufficient Optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions. Subsequently, we apply the Optimality conditions to formulate one parametric dual problem and we prove weak duality, strong duality, and strict converse duality theorems.
Tchemisova T.  One of the best experts on this subject based on the ideXlab platform.

Convex semiinfinite programming: Implicit Optimality criterion based on the concept of immobile indices
'Springer Science and Business Media LLC', 1CoAuthors: Kostyukova O., Tchemisova T., Yermalinskaya S. A.Abstract:We state a new implicit Optimality criterion for convex semiinfinite programming (SIP) problems. This criterion does not require any constraint qualification and is based on concepts of immobile index and immobility order. Given a convex SIP problem with a continuum of constraints, we use an information about its immobile indices to construct a nonlinear programming (NLP) problem of a special form. We prove that a feasible point of the original infinite SIP problem is optimal if and only if it is optimal in the corresponding finite NLP problem. This fact allows us to obtain new efficient Optimality conditions for convex SIP problems using known results of the Optimality theory of NLP. To construct the NLP problem, we use the DIO algorithm. A comparison of the Optimality conditions obtained in the paper with known results is provided

Study of a special nonlinear problem arising in convex semiinfinite programming
'Springer Science and Business Media LLC', 1CoAuthors: Kostyukova O., Tchemisova T., Yermalinskaya S.Abstract:We consider convex problems of semiinfinite programming (SIP) using an approach based on the implicit Optimality criterion. This criterion allows one to replace Optimality conditions for a feasible solution x0 of the convex SIP problem by such conditions for x0 in some nonlinear programming (NLP) problem denoted by NLP(I(x0)). This nonlinear problem, constructed on the base of special characteristics of the original SIP problem, socalled immobile indices and their immobility orders, has a special structure and a diversity of important properties. We study these properties and use them to obtain efficient explicit Optimality conditions for the problem NLP(I(x0)). Application of these conditions, together with the implicit Optimality criterion, gives new efficient Optimality conditions for convex SIP problems. Special attention is paid to SIP problems whose constraints do not satisfy the Slater condition and to problems with analytic constraint functions for which we obtain Optimality conditions in the form of a criterion. Comparison with some known Optimality conditions for convex SIP is provided

Rigidity of abnormal extrema in nonlinear programming problems with equality and inequality constraints
'Elsevier BV', 1CoAuthors: Tchemisova T.Abstract:Optimality conditions for nonlinear problems with equality and inequality constraints are considered. In the case when no constraint qualification (or regularity) is assumed, the Lagrange multiplier corresponding to the objective function can vanish in first order necessary Optimality conditions given by Fritz John and the corresponding extremum is called abnormal. In the paper we consider second order sufficient Optimality conditions that guarantee the rigidity of abnormal extrema (i.e. their isolatedness in the admissible sets)

Sufficient Optimality conditions for convex semiinfinite programming
'Informa UK Limited', 1CoAuthors: Kostyukova O., Tchemisova T.Abstract:We consider a convex semiinfinite programming (SIP) problem whose objective and constraint functions are convex w.r.t. a finitedimensional variable x and whose constraint function also depends on a socalled index variable that ranges over a compact set inR. In our previous paper [O.I.Kostyukova,T.V. Tchemisova, and S.A.Yermalinskaya, On the algorithm of determination of immobile indices for convex SIP problems, IJAMAS Int. J. Math. Stat. 13(J08) (2008), pp. 13–33], we have proved an implicit Optimality criterion that is based on concepts of immobile index and immobility order. This criterion permitted us to replace the Optimality conditions for a feasible solution x0 in the convex SIP problem by similar conditions for x0 in certain finite nonlinear programming problems under the assumption that the active index set is finite in the original semiinfinite problem. In the present paper, we generalize the implicit Optimality criterion for the case of an infinite active index set and obtain newfirst and secondorder sufficient Optimality conditions for convex semiinfinite problems. The comparison with some other known Optimality conditions is provided

On a constructive approach to Optimality conditions for convex SIP problems with polyhedral index sets
'Informa UK Limited', 1CoAuthors: Tchemisova T., Olga KostyukovaAbstract:In the paper,we consider a problem of convex SemiInfinite Programming with an infinite index set in the form of a convex polyhedron. In study of this problem, we apply the approach suggested in our recent paper [Kostyukova OI, Tchemisova TV. Sufficient Optimality conditions for convex Semi Infinite Programming. Optim. Methods Softw. 2010;25:279–297], and based on the notions of immobile indices and their immobility orders. The main result of the paper consists in explicit Optimality conditions that do not use constraint qualifications and have the form of criterion. The comparison of the new Optimality conditions with other known results is provided
Takanori Sugiyama  One of the best experts on this subject based on the ideXlab platform.

adaptive experimental design for one qubit state estimation with finite data based on a statistical update criterion
Physical Review A, 2012CoAuthors: Takanori Sugiyama, Peter S Turner, Mio MuraoAbstract:We consider 1qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the averagevarianceOptimality (AOptimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A optimization is a nonlinear minimization problem; however, we find an analytic solution for 1qubit state estimation using projective measurements, reducing computational effort. We compare numerically the performances of two adaptive and two nonadaptive schemes for finite data sets and show that the AOptimality criterion gives more precise estimates than standard quantum tomography.

adaptive experimental design for one qubit state estimation with finite data based on a statistical update criterion
Physical Review A, 2012CoAuthors: Takanori Sugiyama, Peter S Turner, Mio MuraoAbstract:We consider 1qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the averagevarianceOptimality (AOptimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, Aoptimization is a nonlinear minimization problem; however, we find an analytic solution for 1qubit state estimation using projective measurements, reducing computational effort. We compare numerically two adaptive and two nonadaptive schemes for finite data sets and show that the AOptimality criterion gives more precise estimates than standard quantum tomography.
Hangchin Lai  One of the best experts on this subject based on the ideXlab platform.

necessary and sufficient conditions for minimax fractional programming
Journal of Mathematical Analysis and Applications, 1999CoAuthors: Hangchin Lai, J. C. Liu, Kensuke TanakaAbstract:We establish the necessary and sufficient Optimality conditions for a class of nondifferentiable minimax fractional programming problems solving generalized convex functions. Subsequently, we apply the Optimality conditions to formulate one parametric dual problem and we prove weak duality, strong duality, and strict converse duality theorems.