The Support Vector Machine (SVM) is a powerful and widely used classification algorithm. Its performance is well known to be impacted by a tuning parameter which is frequently selected by cross-validation. This paper uses the Karush-Kuhn-Tucker conditions to provide rigorous mathematical proof for new insights into the behavior of SVM in the large and small tuning parameter regimes. These insig...

The aim of present paper is to study a constrained programming with generalized $alpha-$univex fuzzy mappings. In this paper we introduce the concepts of $alpha-$univex, $alpha-$preunivex, pseudo $alpha-$univex and $alpha-$unicave fuzzy mappings, and we discover that $alpha-$univex fuzzy mappings are more general than univex fuzzy mappings. Then, we discuss the relationships of generalized $alp...

<abstract><p>We report a continuum theory for 2D strain gradient materials accounting class of dissipation phenomena. The description is constructed by means (reversible) placement function and (irreversible) damage plastic functions. Besides, expressions elastic energies have been assumed as well the postulation hemi-variational principle. No flow rules deformation also compatible,...

This paper is devoted to provide sufficient Karush Kuhn Tucker (in short, KKT) conditions of optimality second-order for a set-valued fractional minimax problem. In addition, we define duals the types Mond-Weir and Wolfe Further obtain theorems duality under contingent epi-derivative together with generalized cone convexity suppositions second-order.

To get positive Lagrange multipliers associated with each of the objective function, Maeda [Constraint qualification in multiobjective optimization problems: Differentiable case, J. Optimization Theory Appl., 80, 483–500 (1994)], gave some special sets and derived some generalized regularity conditions for first-order Karush–Kuhn– Tucker (KKT)-type necessary conditions of multiobjective optimiz...

In this paper, we consider a nonsmooth multiobjective semi-infinite programming problem with vanishing constraints (MOSIPVC). We introduce stationary conditions for the MOSIPVCs and establish the strong Karush-Kuhn-Tucker type sufficient optimality conditions for the MOSIPVC under generalized convexity assumptions.

The evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an -approximate first-order critical point of the problem can be computed in order O( 1−2(p+1)/p) evaluations of the problem’s function and their first p derivatives. This is achieved by using a two-phases algorithm inspired by Cartis,...

In this paper we investigate how to efficiently apply ApproximateKarush-Kuhn-Tucker (AKKT) proximity measures as stopping criteria for optimization algorithms that do not generate approximations to Lagrange multipliers, in particular, Genetic Algorithms. We prove that for a wide range of constrained optimization problems the KKT error measurement tends to zero. We also develop a simple model to...

In this paper we present the convergence analysis of the inexact infeasible path-following (IIPF) interior point algorithm. In this algorithm the preconditioned conjugate gradient method is used to solve the reduced KKT system (the augmented system). The augmented system is preconditioned by using a block triangular matrix. The KKT system is solved approximately. Therefore, it becomes necessary...

Optimization problems are not only formed into a linear programming but also nonlinear programming. In real life, often decision variables restricted on integer. Hence, came the nonlinear programming. One particular form of nonlinear programming is a convex quadratic programming which form the objective function is quadratic and convex and linear constraint functions. In this research designed ...