• Korean Journal of Mathematics
• /
• 제23권2호
• /
• pp.283-291
• /
• 2015

In the optimal control problem, at first we search the expected optimal solution by using Pontryagin type's necessary conditions called the maximum principle. Next we use the sufficient conditions to conclude that the searched solution is optimal. In this article the sufficient conditions are studied. The value function is used for sufficient conditions.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.85-107
• /
• 2007

In this paper, we develop a fairly large number of sets of global semiparametric sufficient efficiency conditions under various generalized (${\theta},{\eta},{\rho}$)-V-invexity assumptions for a multiobjective fractional programming problem involving arbitrary norms.

• 대한수학회논문집
• /
• 제19권3호
• /
• pp.557-567
• /
• 2004

We prove the sufficient conditions for optimality in differential inclusion problem by using the value function. For this purpose, we assume at first that the value function is locally Lipschitz. Secondly, without this assumption, we use the viability theory.

• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.223-233
• /
• 2008

In this paper we give sufficient conditions for a point to be a solution of an optimization problem in complex space.

• 한국수학교육학회지시리즈D:수학교육연구
• /
• 제15권4호
• /
• pp.327-340
• /
• 2011

In this paper we propose an inquiry task on the subject of congruent triangles. The task deals with conditions that are sufficient for congruency, and conditions that are insufficient. The aim of the task is to find the minimal number of identical components in two triangles that is sufficient to ensure congruency.

• Journal of applied mathematics & informatics
• /
• 제23권1_2호
• /
• pp.1-23
• /
• 2007

The purpose of this paper is to develop a fairly large number of sets of global parametric sufficient optimality conditions under various generalized $({\theta},\;{\eta},\;{\rho})-V-invexity$ assumptions for a discrete minmax fractional programming problem involving arbitrary norms.

• 호남수학학술지
• /
• 제41권2호
• /
• pp.227-242
• /
• 2019

In the present paper, we derive several sufficient conditions for $Carath{\acute{e}}odory$ functions in the open unit disk ${\mathbb{D}}:=\{z{\in}{\mathbb{C}}:{\mid}z{\mid}<1\}$ under the constraint that the second coefficient of the function is preassigned. And, we obtain some sufficient conditions for strongly starlike functions in ${\mathbb{D}}$.

• Journal of applied mathematics & informatics
• /
• 제29권1_2호
• /
• pp.337-349
• /
• 2011

This paper is concerned with deriving necessary and sufficient optimality conditions for a fuzzy linear programming problem. Toward this end, an equivalence between fuzzy and crisp linear programming problems is established by means of a specific ranking function. Under this setting, a main theorem gives optimality conditions which do not seem to be in conflict with the so-called Karush-Kuhn-Tucker conditions for a crisp linear programming problem.

• Journal of the Korean Statistical Society
• /
• 제23권2호
• /
• pp.513-522
• /
• 1994

A multi-dimensional design is most easily constructed via the amalgamation of one-dimensional component block designs. However, not all sets of component designs are compatible to be amalgamated. The conditions for compatibility are related to the concept of a complete matching in a graph. In this paper, we give sufficient conditions for unequal-replicate designs. Two types of conditions are proposed; one is based on the number of verices adjacent to at least one vertex and the other is ona a degree of vertex, in a bipartite graph. The former is an extension of the sufficient conditions of equal-replicate designs given by Dean an Lewis (1988).

• 대한수학회지
• /
• 제37권4호
• /
• pp.625-643
• /
• 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.