Cutting-Planes for Optimization of Convex Functions over Nonconvex Sets

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

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Hermite-Hadamard and simpson-like type inequalities for differentiable p-quasi-convex functions

Filomat ◽

10.2298/fil1719945i ◽

2017 ◽

Vol 31 (19) ◽

pp. 5945-5953 ◽

Cited By ~ 7

Author(s):

İmdat İsçan ◽

Sercan Turhan ◽

Selahattin Maden

Keyword(s):

Convex Functions ◽

Real Numbers ◽

Absolute Value ◽

Special Means ◽

Quasi Convexity

In this paper, we give a new concept which is a generalization of the concepts quasi-convexity and harmonically quasi-convexity and establish a new identity. A consequence of the identity is that we obtain some new general inequalities containing all of the Hermite-Hadamard and Simpson-like type for functions whose derivatives in absolute value at certain power are p-quasi-convex. Some applications to special means of real numbers are also given.

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Weighted version of Hermite–Hadamard type inequalities for geometrically quasi-convex functions and their applications

Journal of Inequalities and Applications ◽

10.1186/s13660-018-1904-7 ◽

2018 ◽

Vol 2018 (1) ◽

Author(s):

Sofian Obeidat ◽

Muhammad Amer Latif

Keyword(s):

Convex Functions ◽

Weighted Version

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Extreme-point solutions in Markov decision processes

Journal of Applied Probability ◽

10.1017/s002190020002413x ◽

1983 ◽

Vol 20 (04) ◽

pp. 835-842

Author(s):

David Assaf

Keyword(s):

Convex Function ◽

Extreme Point ◽

Markov Decision Processes ◽

Convex Functions ◽

Sufficient Conditions ◽

Decision Processes ◽

Markov Decision ◽

Full Solution

The paper presents sufficient conditions for certain functions to be convex. Functions of this type often appear in Markov decision processes, where their maximum is the solution of the problem. Since a convex function takes its maximum at an extreme point, the conditions may greatly simplify a problem. In some cases a full solution may be obtained after the reduction is made. Some illustrative examples are discussed.

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