We develop an iterative method for solving the KKT system of the semi-infinite programming (SIP) problem. At each iteration, we solve the KKT system of a nonlinear programming problem with finite constraints by a semismooth Newton method. The algorithm either terminates at a KKT point of the SIP problem in finitely many iterations or generates an infinite sequence of iterates whose any accumula...

We consider Karush-Kuhn-Tucker (KKT) systems, which depend on a parameter. Our contribution concerns with the existence of solution of the directionally perturbed KKT system, approximating the given primaldual base solution. To our knowledge, we give the first explicit result of this kind in the situation where the multiplier associated with the base primal solution may not be unique. The condi...

This paper studies the representation of a positive polynomial f(x) on a noncompact semialgebraic set S = {x ∈ R : g1(x) ≥ 0, · · · , gs(x) ≥ 0} modulo its KKT (Karush-KuhnTucker) ideal. Under the assumption that the minimum value of f(x) on S is attained at some KKT point, we show that f(x) can be represented as sum of squares (SOS) of polynomials modulo the KKT ideal if f(x) > 0 on S; further...

We consider the solution of generalized Nash equilibrium problems by concate-nating the KKT optimality conditions of each player’s optimization problem into a singleKKT-like system. We then propose two approaches for solving this KKT system. The firstapproach is rather simple and uses a merit-function/equation-based technique for the solutionof the KKT system. The second approac...

We consider the solution of generalized Nash equilibrium problems by concate-nating the KKT optimality conditions of each player’s optimization problem into a singleKKT-like system. We then propose two approaches for solving this KKT system. The firstapproach is rather simple and uses a merit-function/equation-based technique for the solutionof the KKT system. The second approac...

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...