In this paper, a fast bounded parametric margin  -support vector machine (BP- SVM) for classification is proposed. Different from the parametric margin  -support vector machine (par- -SVM), the BP- -SVM maximizes a bounded parametric margin, and consequently the successive overrelaxation (SOR) technique could be used to solve our dual problem as opposed solving the standard quadratic progr...

Let F be a subset of the n-dimensional Euclidean spaceR represented in terms of a compact convex subset C0 and a set PF of nitely or in nitely many quadratic functions on R such that F = fx 2 C0 : p(x) 0 (8p( ) 2 PF )g. In this paper, we investigate some fundamental properties related to the nite convergence of the successive SDP (semide nite programming) relaxation method proposed by the autho...

This paper presents a fuzzy goal programming (FGP) methodology for solving bi-level quadratic programming (BLQP) problems. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vec...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...

Sequential (or Successive) Quadratic Programming (SQP) is a technique for the solution of Nonlinear Programming (NLP) problems. It is, as we shall see, an idealized concept, permitting and indeed necessitating many variations and modifications before becoming available as part of a reliable and efficient production computer code. In this monograph we trace the evolution of the SQP method throug...