The conjugate of the pointwise maximum of two convex functions revisited

Some Properties of Certain Subclasses of Close-to-Convex and Quasi-convex Functions with Respect to 2k-Symmetric Conjugate Points

SOLVING FUZZY LINEAR PROGRAMMING PROBLEMS WITH LINEAR MEMBERSHIP FUNCTIONS-REVISITED

Recently, Gasimov and Yenilmez proposed an approach for solving two kinds of fuzzy linear programming (FLP) problems. Through the approach, each FLP problem is first defuzzified into an equivalent crisp problem which is non-linear and even non-convex. Then, the crisp problem is solved by the use of the modified subgradient method. In this paper we will have another look at the earlier defuzzifi...

On the Pointwise Maximum of Convex Functions

We study the conjugate of the maximum, f ∨ g, of f and g when f and g are proper convex lower semicontinuous functions on a Banach space E. We show that (f ∨g)∗∗ = f∗∗ ∨g∗∗ on the bidual, E∗∗, of E provided that f and g satisfy the Attouch-Brézis constraint qualification, and we also derive formulae for (f ∨ g)∗ and for the “preconjugate” of f∗ ∨ g∗.

Two Settings of the Dai-Liao Parameter Based on Modified Secant Equations

Following the setting of the Dai-Liao (DL) parameter in conjugate gradient (CG) methods‎, ‎we introduce two new parameters based on the modified secant equation proposed by Li et al‎. ‎(Comput‎. ‎Optim‎. ‎Appl‎. ‎202:523-539‎, ‎2007) with two approaches‎, ‎which use an extended new conjugacy condition‎. ‎The first is based on a modified descent three-term search direction‎, ‎as the descent Hest...

Sweep Line Algorithm for Convex Hull Revisited

Convex hull of some given points is the intersection of all convex sets containing them. It is used as primary structure in many other problems in computational geometry and other areas like image processing, model identification, geographical data systems, and triangular computation of a set of points and so on. Computing the convex hull of a set of point is one of the most fundamental and imp...