In this paper we consider the linear symmetric cone programming (SCP). At a KarushKuhn-Tucker (KKT) point of SCP, we present the important equivalent conditions for the nonsingularity of Clarke’s generalized Jacobian of the KKT nonsmooth system, such as primal and dual constraint nondegeneracy, the strong regularity, and the nonsingularity of the B-subdifferential of the KKT system. This affirm...

In this technical note, we suggest a new definition for an approximate KKT point. The concept of approximate KKT point can then be used on iterates (points found by an optimization algorithm) to check whether the iterates lead to a KKT point. We will concentrate on the following simple optimization problem (P): Min f(x) subject to gi(x) ≤ 0, i = 1, 2, . . . ,m. (1) We will assume that f and eac...

In this note, we prove that the KKT mapping for nonlinear semidefinite optimization problem is upper Lipschitz continuous at the KKT point, under the second-order sufficient optimality conditions and the strict Robinson constraint qualification.

Exact data of an electric circuit (EC) model of RLC (resistor, inductor, capacitor) elements representing rational immittance of LTI (linear, time invariant) systems are numerically Fourier transformed to demonstrate within error bounds applicability of the Hilbert integral tranform (HT) and Kramers-Kronig (KK) integral tranform (KKT) method. Immittance spectroscopy (IS) data are validated for ...

We consider the convex optimization problem minx{f(x) : gj(x) ≤ 0, j = 1, . . . , m} where f is convex, the feasible set K is convex and Slater’s condition holds, but the functions gj ’s are not necessarily convex. We show that for any representation of K that satisfies a mild nondegeneracy assumption, every minimizer is a Karush-Kuhn-Tucker (KKT) point and conversely every KKT point is a minim...

In this paper we study first order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various wellknown constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs take...

Approximate optimality conditions for a class of nonconvex semi-infinite programs involving support functions are given. The objective function and the constraint functions are locally Lipschitz functions on n . By using a Karush-Kuhn-Tucker KKT condition, we deduce a necessary optimality condition for local approximate solutions. Then, generalized KKT conditions for the problems are proposed. ...

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...