• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.235-249
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• 2013

It is well known that each kernel function defines primal-dual interior-point method (IPM). Most of polynomial-time interior-point algorithms for linear optimization (LO) are based on the logarithmic kernel function ([9]). In this paper we define new eligible kernel function and propose a new search direction and proximity function based on this function for LO problems. We show that the new algorithm has $\mathcal{O}(({\log}\;p)^{\frac{5}{2}}\sqrt{n}{\log}\;n\;{\log}\frac{n}{\epsilon})$ and $\mathcal{O}(q^{\frac{3}{2}}({\log}\;p)^3\sqrt{n}{\log}\;\frac{n}{\epsilon})$ iteration complexity for large- and small-update methods, respectively. These are currently the best known complexity results for such methods.

• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.395-408
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• 2024

There have been numerous studies on the characteristics of the solutions of ordinary differential equations for optimization methods, including gradient descent methods and alternating direction methods of multipliers. To investigate computer simulation of ODE solutions, we need to trace pseudo-orbits by real orbits and it is called shadowing property in dynamics. In this paper, we demonstrate that the flow induced by the alternating direction methods of multipliers (ADMM) for a C² strongly convex objective function has the eventual shadowing property. For the converse, we partially answer that convexity with the eventual shadowing property guarantees a unique minimizer. In contrast, we show that the flow generated by a second-order ODE, which is related to the accelerated version of ADMM, does not have the eventual shadowing property.

• IE interfaces
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• v.21 no.1
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• pp.1-7
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• 2008

In this paper we study the Minimum Edge Addition Problem(MEAP) to decrease the diameter of a graph. MEAP can be used for improving the serviceability of telecommunication networks with a minimum investment. MEAP is an NP-hard optimization problem. We present two mathematical programming models : One is a multi-commodity flow formulation and the other is a path partition formulation. We propose a branch-and-price algorithm to solve the path partition formulation to the optimality. We develop a polynomial time column generation sub-routine conserving the mathematical structure of a sub problem for the path partition formulation. Computational experiments show that the path partition formulation is better than the multi-commodity flow formulation. The branch-and-price algorithm can find the optimal solutions for the immediate size graphs within reasonable time.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1523-1537
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• 2022

We present a new square root algorithm in finite fields which is a variant of the Pocklington-Peralta algorithm. We give the complexity of the proposed algorithm in terms of the number of operations (multiplications) in finite fields, and compare the result with other square root algorithms, the Tonelli-Shanks algorithm, the Cipolla-Lehmer algorithm, and the original Pocklington-Peralta square root algorithm. Both the theoretical estimation and the implementation result imply that our proposed algorithm performs favorably over other existing algorithms. In particular, for the NIST suggested field P-224, we show that our proposed algorithm is significantly faster than other proposed algorithms.

• Journal of the Korean Society of Marine Environment & Safety
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• v.24 no.3
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• pp.295-301
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• 2018

This study compares optimization algorithms for efficient estimations of ship's hydrodynamic coefficients. Two constrained algorithms, the interior point and the sequential quadratic programming, are compared for the estimation. Mathematical optimization is designed to get optimal hydrodynamic coefficients for modelling a ship, and benchmark data are collected from sea trials of a training ship. A calibration for environmental influence and a sensitivity analysis for efficiency are carried out prior to implementing the optimization. The optimization is composed of three steps considering correlation between coefficients and manoeuvre characteristics. Manoeuvre characteristics of simulation results for both sets of optimized coefficients are close to each other, and they are also fit to the benchmark data. However, this similarity interferes with the comparison, and it is supposed that optimization conditions, such as designed variables and constraints, are not sufficient to compare them strictly. An enhanced optimization with additional sea trial measurement data should be carried out in future studies.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.403-416
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• 2013

This paper describes new optimization strategy that offers significant improvements in performance over existing methods for geometry design of frame structures. In this study, an imperialist competitive algorithm (ICA) and ant colony optimization (ACO) are combined to reach to an efficient algorithm, called Imperialist Competitive Ant Colony Optimization (ICACO). The ICACO applies the ICA for global optimization and the ACO for local search. The results of optimal geometry for three benchmark examples of frame structures, demonstrate the effectiveness and robustness of the new method presented in this work. The results indicate that the new technique has a powerful search strategies due to the modifications made in search module of ICACO. Higher rate of convergence is the superiority of the presented algorithm in comparison with the conventional mathematical methods and non hybrid heuristic methods such as ICA and particle swarm optimization (PSO).

• Journal of Distribution Science
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• v.15 no.2
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• pp.15-20
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• 2017

Purpose - This paper aims to suggest a delivery constrained internet shopping optimization problem (DISOP) which must be solved for online recommendation system to provide a customized service considering cost and delivery conditions at the same time. Research design, data, and methodology - To solve a (DISOP), we propose a multi-objective formulation and a solution approach. By using a commercial optimization software (LINDO), a (DISOP) can be solved iteratively and a pareto optimal set can be calculated for real-sized problem. Results - We propose a new research problem which is different with internet shopping optimization problem since our problem considers not only the purchasing cost but also delivery conditions at the same time. Furthermore, we suggest a multi-objective mathematical formulation for our research problem and provide a solution approach to get a pareto optimal set by using numerical example. Conclusions - This paper proposes a multi-objective optimization problem to solve internet shopping optimization problem with delivery constraint and a solution approach to get a pareto optimal set. The results of research will contribute to develop a customized comparison and recommendation system to help more easy and smart online shopping service.

• Structural Engineering and Mechanics
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• v.52 no.2
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• pp.405-426
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• 2014

In this paper, a new meta-heuristic algorithm named Ranked Particles Optimization (RPO), is presented. This algorithm is not inspired from natural or physical phenomena. However, it is based on numerous researches in the field of meta-heuristic optimization algorithms. In this algorithm, like other meta-heuristic algorithms, optimization process starts with by producing a population of random solutions, Particles, located in the feasible search space. In the next step, cost functions corresponding to all random particles are evaluated and some of those having minimum cost functions are stored. These particles are ranked and their weighted average is calculated and named Ranked Center. New solutions are produced by moving each particle along its previous motion, the ranked center, and the best particle found thus far. The robustness of this algorithm is verified by solving some mathematical and structural optimization problems. Simplicity of implementation and reaching to desired solution are two main characteristics of this algorithm.

• Proceedings of the KSME Conference
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• 2004.11a
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• pp.870-875
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• 2004

Current trend of design technologies shows engineers to objectify or automate the given decision-making process. The numerical optimization is an example of such technologies. However, in numerical optimization, the uncertainties are uncontrollable to efficiently objectify or automate the process. To better manage these uncertainties, Taguchi method, reliability-based optimization and robust optimization are being used. To obtain the target performance with the maximum robustness is the main functional requirement of a mechanical system. In this research, the robust design strategy is developed based on the DACE and the global optimization approaches. The DACE modeling, known as the one of Kriging interpolation, is introduced to obtain the surrogate approximation model of the system. The robustness is determined by the DACE model to reduce the real function calculations. The simulated annealing algorithm of global optimization methods is adopted to determine the global robust design of a surrogated model. The mathematical problems and the MEMS design problem are investigated to show the validity of the proposed method.