Standard preconditioners, such as ILU factorizations, often break down in construction for KKT matrices. We compare several approaches for preconditioning KKT systems. The first applies a constraint preconditioner by incorporating robust factored approximations of (BB ) and BB , where B is the (2,1) block of the KKT matrix. In the second approach, we apply permutations and scalings that maximiz...

This paper is devoted to studying the robust isolated calmness of the Karush– Kuhn–Tucker (KKT) solution mapping for a large class of interesting conic programming problems (including most commonly known ones arising from applications) at a locally optimal solution. Under the Robinson constraint qualification, we show that the KKT solution mapping is robustly isolated calm if and only if both t...

In this paper, we establish second-order KKT conditions of a set-valued optimization problem and study Mond-Weir, Wolfe, mixed types duals with the help contingent epiderivative generalized cone convexity assumptions.

Iterative methods are proposed for certain augmented systems of linear equations that arise in interior methods for general nonlinear optimization. Interior methods define a sequence of KKT equations that represent the symmetrized (but indefinite) equations associated with Newton’s method for a point satisfying the perturbed optimality conditions. These equations involve both the primal and dua...

In this article, we discuss an exact algorithm for solving mixed integer concave minimization problems. A piecewise inner-approximation of the function is achieved using auxiliary linear program that leads to a bilevel program, which provides lower bound original problem. The reduced single level formulation with help Karush–Kuhn–Tucker (KKT) conditions. Incorporating KKT conditions lead comple...

In this paper, we study a class of optimization problems, called Mathematical Programs with Cardinality Constraints (MPCaC). This kind problem is generally difficult to deal with, because it involves constraint that not continuous neither convex, but provides sparse solutions. Thereby reformulate MPCaC in suitable way, by modeling as mixed-integer and then addressing its counterpart, which will...

In this paper we study firstand second-order necessary conditions for nonlinear programming problems from the viewpoint of exact penalty functions. By applying the variational description of regular subgradients, we first establish necessary and sufficient conditions for a penalty term to be of KKT-type by using the regular subdifferential of the penalty term. In terms of the kernel of the subd...