• Title, Summary, Keyword: sufficient conditions

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VALUE FUNCTION AND OPTIMALITY CONDITIONS

  • KIM, KYUNG EUNG
    • Korean Journal of Mathematics
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    • v.23 no.2
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    • pp.283-291
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    • 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.

SUFFICIENT CONDITIONS FOR OPTIMALITY IN DIFFERENTIAL INCLUSION UNDER STATE CONSTRAINTS

  • Kim, Kyung-Eung
    • Communications of the Korean Mathematical Society
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    • v.19 no.3
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    • pp.557-567
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    • 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.

Congruent Triangles Sufficient and Insufficient Conditions Suggested Milestones for Inquiry and Discussion

  • Patkin, Dorit;Plaksin, Olga
    • Research in Mathematical Education
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    • v.15 no.4
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    • pp.327-340
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    • 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.

Sufficient Conditions for Compatibility of Unequal-replicate Component Designs

  • Park, Dong-Kwon
    • Journal of the Korean Statistical Society
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    • v.23 no.2
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    • pp.513-522
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    • 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).

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NECESSARY AND SUFFICIENT CONDITIONS FOR THE EXISTENCE OF SOLUTIONS TO OPERATOR EQUATIONS

  • Park, Sehie
    • Bulletin of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.151-155
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    • 1990
  • Recently, H.Z.Ming [7] obtained a necessary and sufficient condition for the existence of a solution to a general operator equation. In the present paper, we obtain such conditions in general forms and give some examples. We begin with the well-known Fan-Browder fixed point theorem, from which we deduce two general theorems on such necessary and sufficient conditiions. We give some examples of such conditions, which are improved versions of fixed point theorems of Halpern-Bergman [5], Ky Fan [3], [4], Kaczynski [6], Reich [9], Schauder [10], Tychonoff [11], and Ming [7]. In fact, we restate Ming's result in its correct form. The following is known as the Fan-Browder fixed point theorem [1], [2].

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ON SUFFICIENT CONDITIONS FOR CARATHÉODORY FUNCTIONS WITH THE FIXED SECOND COEFFICIENT

  • Kwon, Oh Sang
    • Honam Mathematical Journal
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    • v.41 no.2
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    • pp.227-242
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    • 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 ${\mathbb{D}}$.

NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR FUZZY LINEAR PROGRAMMING

  • Farhadinia, Bahram
    • Journal of applied mathematics & informatics
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    • v.29 no.1_2
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    • pp.337-349
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    • 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.

NECESSARY AND SUFFICIENT OPTIMALITY CONDITIONS FOR CONTROL SYSTEMS DESCRIBED BY INTEGRAL EQUATIONS WITH DELAY

  • Elangar, Gamal-N.;Mohammad a Kazemi;Kim, Hoon-Joo
    • Journal of the Korean Mathematical Society
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    • v.37 no.4
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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.

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Some Sufficient Conditions for Output Regulation of Uncertain Nonlinear Systems (불확실 비선형 시스템의 출력제어를 위한 충분조건)

  • 하인중;최종호;고명삼
    • Journal of the Korean Institute of Telematics and Electronics
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    • v.25 no.2
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    • pp.162-167
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    • 1988
  • In this note, we present some sufficient conditions on the structure of modelling uncertainties for output regualtion of uncertain systems. It turns out that these conditions include as special cases the ordinary matching conditions for stage regulation of uncertain systems and the disturbance decoupling condition. the previous restrictions on the structure of modelling uncertainties can be considerably relaxed in the case of output regulation. The significance of out result is illuminated through a simple example.

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