• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.387-399
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• 2015

In this paper, a new smoothing approximation to the l₁ exact penalty function for constrained optimization problems (COP) is presented. It is shown that an optimal solution to the smoothing penalty optimization problem is an approximate optimal solution to the original optimization problem. Based on the smoothing penalty function, an algorithm is presented to solve COP, with its convergence under some conditions proved. Numerical examples illustrate that this algorithm is efficient in solving COP.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1477-1487
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• 2010

In this paper, we give a solving approach based on a logarithmic-exponential multiplier penalty function for the constrained minimization problem. It is proved exact in the sense that the local optimizers of a nonlinear problem are precisely the local optimizers of the logarithmic-exponential multiplier penalty problem.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1533-1539
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• 2011

In this paper, a class of nonlinear bilevel programs, i.e. the lower level problem is linear programs, is considered. Aiming at this special structure, we append the duality gap of the lower level problem to the upper level objective with a penalty and obtain a penalized problem. Using the penalty method, we give an existence theorem of solution and propose an algorithm. Then, a numerical example is given to illustrate the algorithm.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.759-772
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• 2012

In this paper, semi-infinite constrained programming, a class of constrained nonsmooth optimization problems, are transformed into unconstrained nonsmooth convex programs under the help of exact penalty function. The unconstrained objective function which owns the primal-dual gradient structure has connection with $\mathcal{VU}$-space decomposition. Then a $\mathcal{VU}$-space decomposition method can be applied for solving this unconstrained programs. Finally, the superlinear convergence algorithm is proved under certain assumption.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.4
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• pp.1077-1088
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• 1996

In this paper, we propose a new method to analyze the performance degradation by timing jitters in the receivers of intensity modulation/direct detection digital optical communication systems where pulse-shaping filters are used to minimize intersymbol interference. The results obtained from the proposed analytical method show that conventional analytical methods underestimate the influence of timing jitters on the receiver performance. Using the proposed anlaytical method, we derive an analytic equation for approximated power penalty due to timing itters and obtain an exact power penalty by numerical analyses. Assuming Gaussian or uniform probability density function for timing jitters, we also show that assumption of Gaussian distribution for timing jitters yields more performance degration than that of uniform distribution.

• Korean Management Science Review
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• v.13 no.3
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• pp.187-198
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• 1996

The traveling salesman problem has been studied for many years since the model can be used for various applications such as vehicle routing, job sequencing, clustering a data array, and so on. In this paper one of the typical exact algorithms for TSP, Minty's, will be modified to improve the performance of the algorithm on the applications without losing simplicity. The Little's algorithm gives good results, however, the simple and plain Minty's algorithm for solving shortest-route problems has the most intuitive appeal. The suggested Minty's modification is based on the creation of penalty-values on the matrix of a TSP. Computer experiments are made to verify the effectiveness of the modification.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.11
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• pp.1844-1851
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• 1997

Displacement fields and interface stresses are obtained by modifying the potential energy functional with a penalty function which enforces the continuity of stresses at the interface of two-materials. Based on the displacement field and the interface stresses, a new methodology to generate a continuous stress field over the entire domain including the interface of the dissimilar materials has been proposed by combining the L$^{2}$ projection method of stress-smoothing and the Loubignac's iterative method of improving the displacement field. Stress analysis was carried out on two examples which are made of highly dissimilar materials. As a result of the analysis, it is found that the proposed method provides improved continuity of the stress field over the entire domain as well as predicting accurate nodal stresses at the interface. In contrast, the conventional displacement-based finite element method provides significant stress discontinuties at the interfaces. In addition, it was found that the total strain energy evaluated from the improved continuous stress field converge to the exact value as increasing the number of iterations in the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.22 no.4
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• pp.811-825
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• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• Journal of information and communication convergence engineering
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• v.7 no.3
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• pp.372-376
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• 2009

In this paper, new and simple optical transmission link with fixed dispersion management (DM) scheme, i.e., pre(post) compensation and residual dispersion per span (RDPS) are fixed to net residual dispersion (NRD) = 0 ps/nm, and optical phase conjugator (OPC) having optimal position depending on launch power in WDM transmission system is proposed. Also, effective launch power range of WDM channels resulting 1 dB eye opening penalty (EOP) is induced as a function of OPC position. First, it is confirmed that, for applying DM into WDM transmission link fixed pre(post)compensation and RDPS, which are independence on exact system parameters except launch power, sufficiently are used in WDM links, but OPC with optimal position is needed for effective compensating impairments of WDM channels. And, it is confirmed that effective launch power is broader in case of RDPS = 100 ps/nm than in RDPS = 50 ps/nm. But, it is shown that the best OPC position offset is -0.6 km from a point of view of power window, which is defined as difference between maximum and minimum effective launch power.

• Nuclear Engineering and Technology
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• v.30 no.3
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• pp.202-211
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• 1998

Interfacial stresses at two-material interfaces and initial displacement field over the entire domain are obtained by modifying the potential energy functional with a penalty function, which enforces continuity of the stresses at the interface of two materials. Based on the initial displacement field and interfacial stresses, a new methodology to generate a continuous stress field over the entire domain has been proposed by combining the modified projection method of stress-smoothing and Loubignac's iterative method of improving the displacement field. Stress analysis is carried out on two examples made of dissimilar materials : one is a two-material cantilever composed of highly dissimilar materials and the other is a zirconium-lined cladding tube made of slightly dissimilar materials. Results of the analysis show that the proposed method provides an improved continuous stress field over the entire domain, and accurately predicts the nodal stresses at the interface, while the conventional displacement-based finite element method produces significant stress discontinuities at the interface. In addition, the total strain energy evaluated from the improved continuous stress field converges to the exact value in a few iterations.