• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1157-1165
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• 2011

The Karush-Kuhn-Tucker (KKT) necessary optimality conditions for nonlinear differentiable programming problems are also sufficient under suitable convexity assumptions. The KKT conditions in multiobjective programming problems with interval-valued objective and constraint functions are derived in this paper. The main contribution of this paper is to obtain the Pareto optimal solutions by resorting to the sufficient optimality condition.

• 대한수학회지
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• 제37권4호
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• pp.625-643
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• 2000

In this paper we formulate an optimal control problem governed by time-delay Volterra integral equations; the problem includes control constraints as well as terminal equality and inequality constraints on the terminal state variables. First, using a special type of state and control variations, we represent a relatively simple and self-contained method for deriving new necessary conditions in the form of Pontryagin minimum principle. We show that these results immediately yield classical Pontryagin necessary conditions for control processes governed by ordinary differential equations (with or without delay). Next, imposing suitable convexity conditions on the functions involved, we derive Mangasarian-type and Arrow-type sufficient optimality conditions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1535-1544
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• 2010

Sufficient optimality conditions for a class of generalized non-differentiable fractional optimization programming problems are established. Moreover, we prove the weak and strong duality theorems under (V, $\rho$)-invexity assumption.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1992년도 하계학술대회 논문집 A
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• pp.386-390
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• 1992

Algorithmic or kinematic singularities are inevitably a introduced if optimality criteria or augmented kinematic equations are used to resolve the redundancy of almost any manipulator with rotary joints. In this paper, a sufficient condition for a singularity-free optimal solution of the kinematic control of a redundant manipulator is derived and, specifically, algorithmic singularities are analyzed for optimality-based methods. A singularity-free space (SFS) to characterize the performance of a secondary task for a redundant manipulator using the sufficient condition for a redundant manipulator is defined. The SFS is a set of regions classified by the loci of configurations satisfying the inflection condition for manipulability measure in the Configuration space. Using SFS, the topological property of the Configuration space and the invertible workspace without singularities are analyzed.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.365-374
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• 2009

Under certain conditions, we use augmented Lagrangians to transform a class of generalized semi-infinite min-max problems into common semi-infinite min-max problems, with the same set of local and global solutions. We give two conditions for the transformation. One is a necessary and sufficient condition, the other is a sufficient condition which can be verified easily in practice. From the transformation, we obtain a new first-order optimality condition for this class of generalized semi-infinite min-max problems.

• 대한수학회보
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• 제23권2호
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• pp.141-148
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• 1986

In [1], M. Guignard considered a constraint set in a Banach space, which is similar to that in [2] and gave a first order necessary optimality condition which generalized the Kuhn-Tucker conditions [3]. Sufficiency is proved for objective functions which is either pseudoconcave [5] or quasi-concave [6] where the constraint sets are taken pseudoconvex. In this note, we consider a psedoconvex programming problem in a Hilbert space. Constraint set in a Hillbert space being pseudoconvex and the objective function is restrained by an operator equation. Then we use the methods similar to that in [1] and [6] to obtain a necessary and sufficient optimality condition.

• 대한수학회지
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• 제44권4호
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• pp.971-985
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• 2007

A sequential optimality condition characterizing the efficient solution without any constraint qualification for an abstract convex vector optimization problem is given in sequential forms using subdifferentials and ${\epsilon}$-subdifferentials. Another sequential condition involving only the subdifferentials, but at nearby points to the efficient solution for constraints, is also derived. Moreover, we present a proposition with a sufficient condition for an efficient solution to be properly efficient, which are a generalization of the well-known Isermann result for a linear vector optimization problem. An example is given to illustrate the significance of our main results. Also, we give an example showing that the proper efficiency may not imply certain closeness assumption.

• 제어로봇시스템학회논문지
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• 제20권5호
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• pp.526-532
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• 2014

In this paper, we present and analyze a LQ (Linear Quadratic) inverse optimal state-consensus protocol for continuous-time multi-agent systems with undirected graph topology. By Lyapunov analysis of the state-consensus error dynamics, we show the sufficient conditions on the algebraic connectivity of the graph to guarantee LQ inverse optimality and closed-loop stability. A more relaxed stability condition is also provided in terms of the algebraic connectivity. Finally, a formation control protocol for multiple mobile robots is proposed based on the target LQ inverse optimal consensus protocol, and the simulation results are provided to verify the performance of the proposed LQ inverse formation control method.

• 한국정보통신학회논문지
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• 제11권1호
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• pp.181-190
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• 2007

본 논문에서는 지능형 선박의 실시간 장애물회피를 위한 충돌회피시스템을 논한다. 다른 무인자율항체들의 충돌회피시스템과는 달리 지능형 선박의 충돌회피시스템은 목적지까지의 합리적이고 안전한 경로를 통한 충돌회피뿐만 아니라 해양을 항해하는 모든 선박이 준수해야하는 국제해상충돌예방규칙(COLRECs, International Regulations for Preventing Collisions at Sea)을 반영해야한다. 목적지까지의 합리적이고 안전한 경로를 통한 충돌회피라는 일반적인 충돌회피시스템의 목표를 달성하기 위해 BK-곱에 기반한 휴리스틱 탐색기법을 채용하며, 또 다른 목표인 COLREGs의 준수를 위해 충돌회피를 위한 규칙을 적용하는 지식기반시스템을 채용한다. 제안된 충돌회피시스템의 성능검증을 위해 COLREGs에 명시된 여러 가지 조우상황을 설정한 시나리오를 이용하여 최적성과 안정성 관점에서 시뮬레이션을 수행하고 그 결과를 $A^{\ast}$ 탐색기법과 비교한다. 시뮬레이션을 통해 제안된 충돌회피시스템이 지능형 선박의 실용적이고 효율적인 실시간 충돌회피시스템으로 적합함을 확인하였다.