• ETRI Journal
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• v.29 no.1
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• pp.50-58
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• 2007

Robust adaptive beamforming based on worst-case performance optimization is investigated in this paper. It improves robustness against steering vector mismatches by the approach of diagonal loading. A closed-form solution to optimal loading is derived after some approximations. Besides reducing the computational complexity, it shows how different factors affect the optimal loading. Based on this solution, a performance analysis of the beamformer is carried out. As a consequence, approximated closed-form expressions of the source-of-interest power estimation and the output signalto-interference-plus-noise ratio are presented in order to predict its performance. Numerical examples show that the proposed closed-form expressions are very close to their actual values.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.99-107
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• 2007

We consider (worst-case) robust optimization versions of the Economic Order Quantity (EOQ) model with decreasing cost functions. Two variants of the EOQ model are discussed, in which the purchasing costs are decreasing power functions in either the order quantity or demand rate. We develop the corresponding worst-case robust optimization models of the two variants, where the parameters in the purchasing cost function of each model are uncertain but known to lie in an ellipsoid. For the robust EOQ model with the purchasing cost being a decreasing function of the demand rate, we derive the analytical optimal solution. For the robust EOQ model with the purchasing cost being a decreasing function of the order quantity, we prove that it is a convex optimization problem, and thus lends itself to efficient numerical algorithms.

• Transactions of the Korean Society of Mechanical Engineers
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• v.13 no.3
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• pp.554-560
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• 1989

An optimal design technique is used as a systematic approach to analyze the worst case of a circulating type ropeway for a given geometry and operating conditions. Worst case is meant here the case when the positions and weights of the cars are so conditioned that the minimum of all the reaction forces between the main rope and the towers is minimum. In the course of this study, a general theory for the deflections and tensions of the main rope were also derived taking into account of the variation of the weights and positions of the individual cars. And through an analysis of example ropeways, some general conditions for the worst case are deduced.

• Journal of Communications and Networks
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• v.16 no.1
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• pp.45-55
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• 2014

The paper investigates the problem of designing the multiple-antenna relay in a two-way relay network by taking into account the imperfect channel state information (CSI). The objective is to design the multiple-antenna relay based upon the CSI estimates, where the estimation errors are included to attain the robust design under the worst-case philosophy. In particular, the worst-case transmit power at the multiple-antenna relay is minimized while guaranteeing the worst-case quality of service requirements that the received signal-to-noise ratio (SNR) at both sources are above a prescribed threshold value. Since the worst-case received SNR expression is too complex for subsequent derivation and processing, its lower bound is explored instead by minimizing the numerator and maximizing the denominator of the worst-case SNR. The aforementioned problem is mathematically formulated and shown to be nonconvex. This motivates the pursuit of semidefinite relaxation coupled with a randomization technique to obtain computationally efficient high-quality approximate solutions. This paper has shown that the original optimization problem can be reformulated and then relaxed to a convex problem that can be solved by utilizing suitable randomization loop. Numerical results compare the proposed multiple-antenna relay with the existing nonrobust method, and therefore validate its robustness against the channel uncertainty. Finally, the feasibility of the proposed design and the associated influencing factors are discussed by means of extensive Monte Carlo simulations.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.56-59
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• 1996

Worst-case state estimation will be proposed in this paper. By using the worst-case disturbance and worst-case state estimation, we can obtain right/left constrained coprime factors. If constrained coprime factors are used in designing a controller, the infinity-norm of closed-loop transfer matrix can be smaller than any constant .gamma.(> .gamma.$_{opt}$) without matrix dilation optimization. The derivation of left/right constrained coprime factors is achieved by doubly coprime factorization for the plant constrained by the infinity norm. And the parameterization of stabilizing controllers gives us easily understanding for H$_{\infty}$ control theory.ry.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.2
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• pp.93-111
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• 2010

The purpose of this paper is to obtain new complexity results for a second-order cone optimization (SOCO) problem. We define a proximity function for the SOCO by a kernel function. Furthermore we formulate an algorithm for a large-update primal-dual interior-point method (IPM) for the SOCO by using the proximity function and give its complexity analysis, and then we show that the new worst-case iteration bound for the IPM is $O(q\sqrt{N}(logN)^{\frac{q+1}{q}}log{\frac{N}{\epsilon})$, where $q{\geqq}1$.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.67 no.6
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• pp.708-714
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• 2018

Islanded operation of a microgrid can ensure the reliable operation of the system when a large accident occurs in the main grid. However, because the generation capability of a microgrid is typically limited, a microgrid operator should take islanded operation risk into account in scheduling its generation resources. To address this problem, in this paper we have proposed two unit commitment formulations based on the islanding scenario that reflect the expected and worst-case values of the islanded operation risk. An optimal resource scheduling strategy is obtained for the microgrid operator by solving these optimization problem, and the effectiveness of the proposed method is investigated by numerical simulations.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.15-15
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• 2003

We provide some recent results of approximation algorithms for solving Markov Games and discuss their applications to problems that arise in Computer Science. We consider a receding horizon approach as an approximate solution to two-person zero-sum Markov games with an infinite horizon discounted cost criterion. We present error bounds from the optimal equilibrium value of the game when both players take “correlated” receding horizon policies that are based on exact or approximate solutions of receding finite horizon subgames. Motivated by the worst-case optimal control of queueing systems by Altman, we then analyze error bounds when the minimizer plays the (approximate) receding horizon control and the maximizer plays the worst case policy. We give two heuristic examples of the approximate receding horizon control. We extend “parallel rollout” and “hindsight optimization” into the Markov game setting within the framework of the approximate receding horizon approach and analyze their performances. From the parallel rollout approach, the minimizing player seeks to combine dynamically multiple heuristic policies in a set to improve the performances of all of the heuristic policies simultaneously under the guess that the maximizing player has chosen a fixed worst-case policy. Given $\varepsilon$>0, we give the value of the receding horizon which guarantees that the parallel rollout policy with the horizon played by the minimizer “dominates” any heuristic policy in the set by $\varepsilon$, From the hindsight optimization approach, the minimizing player makes a decision based on his expected optimal hindsight performance over a finite horizon. We finally discuss practical implementations of the receding horizon approaches via simulation and applications.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.8
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• pp.2840-2853
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• 2015

A major challenge in network service providers is to provide adequate resources in service level agreements based on forecasts of future demands. In this paper, we address the problem of capacity provisioning in a network subject to demand uncertainty such that a network coded multicast is applied as the data delivery mechanism with limited budget to purchase extra capacity. We address some particular type of uncertainty sets that obtain a tractable constrained capacity provisioning problem. For this reason, we first formulate a mathematical model for the problem under uncertain demand. Then, a robust optimization model is proposed for the problem to optimize the worst-case system performance. The robustness and effectiveness of the developed model are demonstrated by numerical results. The robust solution achieves more than 10% reduction and is better than the deterministic solution in the worst case.

• JSTS:Journal of Semiconductor Technology and Science
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• v.5 no.4
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• pp.229-236
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• 2005

This paper presents a system level architecture evaluation technique that leverages transaction level modeling but also significantly extends it to the realm of system level performance evaluation. A major issue lies with the modeling effort. To reduce the modeling effort the proposed technique develops the concept of worst case scenarios. Since the memory controller is often found to be an important component that critically affects the system performance and thus needs optimization, the paper further addresses how to evaluate and optimize the memory controllers, focusing on the test environment and the methodology. The paper also presents an industrial case study using a real state-of-the-art design. In the case study, it is reported that the proposed technique has helped successfully find the performance bottleneck and provide appropriate feedback on time.