11 research outputs found
Generalized convexities and generalized gradients based on algebraic operations
AbstractIn this paper, we investigate properties of generalized convexities based on algebraic operations introduced by Ben Tal [A. Ben Tal, On generalized means and generalized convex functions, J. Optim. Theory Appl. 21 (1977) 1–13] and relations between these generalized convexities and generalized monotonicities. We also discuss the (h,φ)-generalized directional derivative and gradient, and explore the relation between this gradient and the Clarke generalized gradient. Definitions of some generalized averages of the values of a generalized convex function at n equally spaced points based on the algebraic operations are also presented and corresponding results are obtained. Finally, the (φ,γ)-convexity is defined and some properties of (φ,γ)-convex functions are derived
Optimization and Optimal Control
During the last four decades there has been a remarkable development in optimization and optimal control. Due to its wide variety of applications, many scientists and researchers have paid attention to fields of optimization and optimal control. A huge number of new theoretical, algorithmic, and computational results have been observed in the last few years. This book gives the latest advances, and due to the rapid development of these fields, there are no other recent publications on the same topics. Key features: Provides a collection of selected contributions giving a state-of-the-art acco
Piece adding technique for convex maximization problems
Global search algorithm, Local search algorithm, Nonconvex optimization, Convex maximization, Piecewise convex maximization, 90C26, 90C47, 49M05, 49M30,