• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.185-200
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• 2004

A stochastic optimal LQR control problem under some integral quadratic (IQ) constraints is studied, with cross terms in both the cost and the constraint functionals, allowing all the control weighting matrices being indefinite. Sufficient conditions for the well-posedness of this problem are given. When these conditions are satisfied, the optimal control is explicitly derived via dual theory.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.423-432
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• 1998

Let p, q be integers such that 2 $\leq$ p, q $\leq$ n, and let $D_{p, q}$ denote the matrix obtained from $I_{n}$, the identity matrix of order n, by replacing each of the first p columns by an all 1's vector and by replacing each of the first two rows and each of the last q-2 rows by an all 1's vector. In this paper the permanent minimization problem over the face, determined by the matrix $D_{p, q}$, of the polytope of all n $\times$ n doubly stochastic matrices is treated.d.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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• pp.857-867
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• 1995

Throughout this paper, let $M_{mn}(R)$ be the set of all $m \times n$ real matrices, and let $R^n$ the set of all real row vectors with n components.

• 전기의세계
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• v.24 no.5
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• pp.103-106
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• 1975

This Paper deals with an applicatoin of Luenberger Observer to the Linear Stochastic Systems. The basic technique is the use of a matrix version of the Maximum Principle of Pontryagin coupled with the use of gradient matrices to derive the gain matix for minimum error covariance. The optimal observer which is derived turns out to be identical to the well-known Kalman-Bucy Filter.

• Communications of the Korean Mathematical Society
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• v.3 no.1
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• pp.17-24
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• 1988

• Kyungpook Mathematical Journal
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• v.33 no.2
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• pp.173-180
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• 1993

• Kyungpook Mathematical Journal
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• v.32 no.3_spc
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• pp.393-400
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• 1992

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.25 no.4
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• pp.162-172
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• 2021

This paper proposes stochastic methods to find an approximate solution for the L²-Wasserstein least squares problem of Gaussian measures. The variable for the problem is in a set of positive definite matrices. The first proposed stochastic method is a type of classical stochastic gradient methods combined with projection and the second one is a type of variance reduced methods with projection. Their global convergence are analyzed by using the framework of proximal stochastic gradient methods. The convergence of the classical stochastic gradient method combined with projection is established by using diminishing learning rate rule in which the learning rate decreases as the epoch increases but that of the variance reduced method with projection can be established by using constant learning rate. The numerical results show that the present algorithms with a proper learning rate outperforms a gradient projection method.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1303-1315
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• 2018

For principal component analysis (PCA) to efficiently analyze large scale matrices, it is crucial to find a few singular vectors in cheaper computational cost and under lower memory requirement. To compute those in a fast and robust way, we propose a new stochastic method. Especially, we adopt the stochastic variance reduced gradient (SVRG) method [11] to avoid asymptotically slow convergence in stochastic gradient descent methods. For that purpose, we reformulate the PCA problem as a unconstrained optimization problem using a quadratic penalty. In general, increasing the penalty parameter to infinity is needed for the equivalence of the two problems. However, in this case, exact penalization is guaranteed by applying the analysis in [24]. We establish the convergence rate of the proposed method to a stationary point and numerical experiments illustrate the validity and efficiency of the proposed method.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.825-839
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• 1997

The permanent function on certain faces of the polytope of doubly stochastic matrices are studied. These faces are shown to be barycentric, and the minimum values of permanent are determined.