• 대한수학회보
• /
• 제55권4호
• /
• pp.1303-1315
• /
• 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.

• Smart Structures and Systems
• /
• 제9권3호
• /
• pp.231-251
• /
• 2012

The stochastic optimal control for a piezoelectric spherically symmetric shell subjected to stochastic boundary perturbations is constructed, analyzed and evaluated. The stochastic optimal control problem on the boundary stress output reduction of the piezoelectric shell subjected to stochastic boundary displacement perturbations is presented. The electric potential integral as a function of displacement is obtained to convert the differential equations for the piezoelectric shell with electrical and mechanical coupling into the equation only for displacement. The displacement transformation is constructed to convert the stochastic boundary conditions into homogeneous ones, and the transformed displacement is expanded in space to convert further the partial differential equation for displacement into ordinary differential equations by using the Galerkin method. Then the stochastic optimal control problem of the piezoelectric shell in partial differential equations is transformed into that of the multi-degree-of-freedom system. The optimal control law for electric potential is determined according to the stochastic dynamical programming principle. The frequency-response function matrix, power spectral density matrix and correlation function matrix of the controlled system response are derived based on the theory of random vibration. The expressions of mean-square stress, displacement and electric potential of the controlled piezoelectric shell are finally obtained to evaluate the control effectiveness. Numerical results are given to illustrate the high relative reduction in the root-mean-square boundary stress of the piezoelectric shell subjected to stochastic boundary displacement perturbations by the optimal electric potential control.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제9권1호
• /
• pp.99-110
• /
• 2005

This paper suggests an efficient approach for stochastic bicriteria programming problem (SBCPP) with random variables in both the objective functions and in the right-hand side of the constraints. The suggested approach uses the statistical inference through two different techniques: In one of them, the SBCPP is transformed into an equivalent deterministic bicriteria programming problem (DBCPP), then the nonnegative weighted sum approach will be used to transform the bicriteria programming problem into a single objective programming problem, and the other technique, the nonnegative weighted sum approach is used to transform the SBCPP to an equivalent stochastic single objective programming problem, then apply the same procedure to convert stochastic single objective programming problem into its equivalent deterministic single objective programming problem (DSOPP). In both techniques the resulting problem can be solved as a nonlinear programming problem to get the efficient solutions. Finally, a comparison between the two different techniques is discussed, and illustrated example is given to demonstrate the actual application of these techniques.

• Journal of applied mathematics & informatics
• /
• 제7권2호
• /
• pp.507-516
• /
• 2000

In the present paper we consider a problem of choosing the rational way to carry on the metal processing (the problem of stochastic optimization) and the problem of determing the unknown characteristics of parameters described with random variables.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국제학술편); Seoul National University, Seoul; 20-22 Oct. 1993
• /
• pp.155-159
• /
• 1993

In this paper, we consider the problem of a stochastic optimal switching control, which can be applied to the control of a system with uncertain demand such as a control problem of a power plant. The dynamic programming method is applied for the formulation of the optimal control problem. We solve the system of Quasi-Variational Inequalities(QVI) using an algoritlim which involves the finite difference approximation and contraction mapping method. A mathematical example of the optimal switching control is constructed. The actual performance of the algorithm is also tested through the solution of the constructed example.

• 한국생산제조학회지
• /
• 제9권1호
• /
• pp.45-52
• /
• 2000

The purpose of this research was developing an integrated way to solve two typical tolerance optimization problem i.e. optimal tolerance allotment and design centering. A new problem definition design centering-tolerance allotment problem (DCTA) was proposed here for the first time and solved. Genetic algorithm and coarse Monte Carlo simulation were used to solve the stochastic optimization problem. Optimal costs were compared with the costs from the previous optimization strategies Significant cost reductions were achieved by DCTA scheme.

• 충청수학회지
• /
• 제33권1호
• /
• pp.103-112
• /
• 2020

This paper investigates the portfolio selection problem with flexible labor choice and stochastic income flow where the unit wage flow is governed by a stochastic process. The agent optimally chooses consumption, investment, and labor supply. We derive the closed-form solution by applying a martingale method even with the stochastic income flow.

• Journal of applied mathematics & informatics
• /
• 제26권5_6호
• /
• pp.889-900
• /
• 2008

The problem of scheduling n jobs on a single machine is considered when the machine is subject to stochastic breakdowns. The objective is to minimize the weighted squared deviation of job completion times from a common due date. Two versions of the problem are addressed. In the first one the common due date is a given constant, whereas in the second one the common due date is a decision variable. In each case, a general form of deterministic equivalent of the stochastic scheduling problem is obtained when the counting process N(t) related to the machine uptimes is a Poisson process. It is proved that an optimal schedule must be V-shaped in terms of weighted processing time when the agreeable weight condition is satisfied. Based on the V-shape property, two dynamic programming algorithms are proposed to solve both versions of the problem.

• 한국군사과학기술학회지
• /
• 제22권5호
• /
• pp.667-673
• /
• 2019

We present an orienteering problem with unknown stochastic reward(OPUSR) model for persistent monitoring tasks with unknown event probabilities at each point of interest. Prior studies on orienteering problem for persistent monitoring task assume that rewards and event probabilities are known as a prior. In this paper, we propose a stochastic reward model with unknown event statistics and a path re-planning algorithm based on Bayesian reward inference. Experiments demonstrate the efficiency of our method.

• Earthquakes and Structures
• /
• 제3권5호
• /
• pp.719-747
• /
• 2012

In this paper a novel approach is proposed to address the problem of deriving non-stationary stochastic processes which are compatible in the mean sense with a given (target) response (uniform hazard) spectrum (UHS) as commonly desired in the aseismic structural design regulated by contemporary codes of practice. The appealing feature of the approach is that it is non-iterative and "one-step". This is accomplished by solving a standard over-determined minimization problem in conjunction with appropriate median peak factors. These factors are determined by a plethora of reported new Monte Carlo studies which on their own possess considerable stochastic dynamics merit. In the proposed approach, generation and treatment of samples of the processes individually on a deterministic basis is not required as is the case with the various "two-step" approaches found in the literature addressing the herein considered task. The applicability and usefulness of the approach is demonstrated by furnishing extensive numerical data associated with the elastic design UHS of the current European (EC8) and the Chinese (GB 50011) aseismic code provisions. Purposely, simple and thus attractive from a practical viewpoint, uniformly modulated processes assuming either the Kanai-Tajimi (K-T) or the Clough-Penzien (C-P) spectral form are employed. The Monte Carlo studies yield damping and duration dependent median peak factor spectra, given in a polynomial form, associated with the first passage problem for UHS compatible K-T and C-P uniformly modulated stochastic processes. Hopefully, the herein derived stochastic processes and median peak factor spectra can be used to facilitate the aseismic design of structures regulated by contemporary code provisions in a Monte Carlo simulation-based or stochastic dynamics-based context of analysis.