Computer Aided Optimization Techniques Based on Generalized Convex Maps

New Auxiliary Principle Technique for General Harmonic Directional Variational Inequalities

“…The concept of g-convex (Noor-convex) set C g differs from that of E-convex set introduced by Youness [45]. Cristescu et al [9][10][11] have studied the applications of Noor-convex sets in vectorial optimization problems such as ecologic-economic efficiency, railway transport system,image processing. Cristescu et.…”

“…al. [11] compared these concepts the using the digitization method of the plane R 2 into the grid Z 2 . Definition 2.4.…”

“…For the applications of the harmonic means in circuit theory, numerical analysis, risk analysis and related optimization programming, see [2,4,11,26].…”

“…Note that for α = 0, Algorithm 3.6 is exactly the Algorithm 3.1. Using essentially the technique of Theorem 3.1 and Noor [11], one can study the convergence analysis of Algorithm 3.6.…”

“…This theory's concepts and methods very often need an extension, revision, and adaptation in order to make room for new ideas and handle changing problems. The concept of g-convex sets (general convex sets)was first introduced by Noor [20] in relation to an arbitrary operator g. Cristescu et al [9,11] discusses how important these sets are when solving problems related to optimisation. These applications cover a broad range of fields, such as computer-aided design, and processing of the images for example.…”