Convex hull calculation, which is one of the important topics computer aided geometric design, constitutes starting point this study. hull, has many definitions in literature, was calculated with convex combination approach our From definition all possible sets for given set [13], a body consisting n points obtained. In addition to mathematics and geometry, relationship between special generali...

Simple bilevel problems are optimization in which we want to find an optimal solution inner problem that minimizes outer objective function. Such appear many machine learning and signal processing applications as a way eliminate undesirable solutions. In our work, suggest new approach is designed for with simple functions, such the \(l_1\) norm, not required be either smooth or strongly convex....

The notion of approachability in repeated games with vector payoffs was introduced by Blackwell in the 1950s, along with geometric conditions for approachability and corresponding strategies that rely on computing steering directions as projections from the current average payoff vector to the (convex) target set. Recently, Abernethy, Batlett and Hazan (2011) proposed a class of approachability...

In recent years, the optimization of truss structures has been considered due to their several applications and their simple structure and rapid analysis. DNA computing algorithm is a non-gradient-based method derived from numerical modeling of DNA-based computing performance by new computers with DNA memory known as molecular computers. DNA computing algorithm works based on collective intelli...

In this paper, we consider a class of nonsmooth, nonconvex constrained optimization problems where the objective function may be not Lipschitz continuous and the feasible set is a general closed convex set. Using the theory of the generalized directional derivative and the Clarke tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define...

Let $C_0(alpha)$ denote the class of concave univalent functions defined in the open unit disk $mathbb{D}$. Each function $f in C_{0}(alpha)$ maps the unit disk $mathbb{D}$ onto the complement of an unbounded convex set. In this paper, we study the mapping properties of this class under integral operators.

Given a set S of n points in the plane, an -strongly convex -hull of S is de0ned as a convex polygon P with the vertices taken from S such that no point of S lies farther than outside P and such that even if the vertices of P are perturbed by as much as , P remains convex. This paper presents the 0rst parallel robust method for this generalized convex hull problem (note that the convex hull of ...

In Stolyar (Queueing Systems 50 (2005) 401–457) a dynamic control strategy, called greedy primal-dual (GPD) algorithm, was introduced for the problem of maximizing queueing network utility subject to stability of the queues, and was proved to be (asymptotically) optimal. (The network utility is a concave function of the average rates at which the network generates several “commodities.”) Underl...