• Honam Mathematical Journal
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• v.32 no.4
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• pp.763-767
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• 2010

In this note, we give a solution of a $H^{\infty}$-optimization problem.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.671-676
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• 2018

In this paper we prove that the gradient ideal of a Morse polynomial is radical. This gives a generic class of polynomials whose gradient ideals are radical. As a consequence we reclaim a previous result that the unconstrained polynomial optimization problem for Morse polynomials has a finite convergence.

• Communications of the Korean Mathematical Society
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• v.28 no.3
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• pp.597-602
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• 2013

In this paper, Mond-Weir type duality results for a uncertain multiobjective robust optimization problem are given under generalized invexity assumptions. Also, weak vector saddle-point theorems are obtained under convexity assumptions.

• East Asian mathematical journal
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• v.35 no.3
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• pp.289-296
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• 2019

We establish necessary and sufficient optimality conditions for a nonsmooth fractional robust optimization programming problems. Moreover, we prove the weak and strong duality theorems under (V, ${\rho}$)-invexity assumption.

• East Asian mathematical journal
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• v.39 no.5
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• pp.505-514
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• 2023

In this paper, we consider a second-order cone linear fractional vector optimization problems (FVP), and obtain sequential optimality theorems for (FVP) which hold without any constraint qualification and which are expressed by sequences.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.416-421
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• 2008

A Metropolis genetic algorithm (MGA) is a newly-developed hybrid algorithm combining simple genetic algorithm (SGA) and simulated annealing (SA). In the algorithm, favorable features of Metropolis criterion of SA are incorporated in the reproduction operations of SGA. This way, MGA alleviates the disadvantages of finding imprecise solution in SGA and time-consuming computation in SA. It has been successfully applied and the efficiency has been verified for the practical structural design optimization. However, applicability of MGA for the wider range of problems should be rigorously proved through the solution of mathematical optimization problems. Thus, performances of MGA for the typical mathematical problems are investigated and compared with those of conventional algorithms such as SGA, micro genetic algorithm (${\mu}GA$), and SA. And, for better application of MGA, the effects of acceptance level are also presented. From numerical Study, it is again verified that MGA is more efficient and robust than SA, SGA and ${\mu}GA$ in the solution of mathematical optimization problems having various features.

• Journal of Advanced Marine Engineering and Technology
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• v.40 no.10
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• pp.935-941
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• 2016

Predicting and evaluating ship manoeuvring characteristics are very important not only for the design stage, but also for the existing vessels. There are several ways to predict ship's manoeuvrability and most of them are highly connected with the estimation of hydrodynamic coefficients. This paper presents a new estimation method using the system identification with mathematical algorithms for estimating hydrodynamic coefficient in the ship's mathematical model. Specifically a double ended ferry which equips four azimuth propulsion systems were chosen as benchmark ship and a set of benchmark data which is generated in the fast time simulation software was provided to conduct mathematical optimization process. Also the initial values for the optimization were borrowed from the empirical regression formulas of the simulation software of Rheinmetall Defence ship simulator. Therefore the newly suggested mathematical optimization algorithm gave a successful result for estimation hydrodynamic coefficients. Proper optimization conditions of the objective function and constraints were also verified during the study.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• East Asian mathematical journal
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• v.33 no.3
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• pp.265-269
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• 2017

In this paper, we formulate a sufficient optimality theorem for the robust optimization problem (UP) under (V, ${\rho}$)-invexity assumption. Moreover, we formulate a Mond-Weir type dual problem for the robust optimization problem (UP) and show that the weak and strong duality hold between the primal problems and the dual problems.

• Journal of the Chungcheong Mathematical Society
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• v.27 no.3
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• pp.433-438
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• 2014

A semi-infinite optimization problem involving a quasi-convex objective function and infinitely many convex constraint functions with data uncertainty is considered. A surrogate duality theorem for the semi-infinite optimization problem is given under a closed and convex cone constraint qualification.