Abstract We introduce a flexible, open source implementation that provides the optimal sensitivity of solutions of nonlinear programming (NLP) problems, and is adapted to a fast solver based on a barrier NLP method. The program, called sIPOPT evaluates the sensitivity of the KKT system with respect to model parameters. It is paired with the open-source IPOPT NLP solver and reusesmatrix factoriz...

This paper introduces the research status of convex quadratic bilevel programming at present firstly. Secondly, it analyzes the problem of convex quadratic bilevel programming models, concepts and properties. On this basis, using the optimality conditions of KKT, the problem will be transformed into a single complementary slackness relaxation problem. To solve this problem, we propose an orthog...

In this paper we consider the problem of minimizing a quadratic function with a quadratic constraint. We point out some new properties of the problem. In particular, in the rst part of the paper, we show that (i) the number of values of the objective function at KKT points is bounded by 3n + 1 where n is the dimension of the problem; (ii) given a KKT point that is not a global minimizer, it is ...

The paper rst investigates Newton-type methods for generalized equations with compact solution sets. The analysis of their local convergence behavior is based, besides other conditions, on the upper Lipschitz-continuity of the local solution set mapping of a simply perturbed generalized equation. This approach is then applied to the KKT conditions of a nonlinear program with inequality constrai...

A modiication of the (infeasible) primal{dual interior point method is developed. The method uses multiple corrections to improve the centrality of the current iterate. The maximum number of corrections the algorithm is encouraged to make depends on the ratio of the eeorts to solve and to factorize the KKT systems. For any LP problem, this ratio is determined right after preprocessing the KKT s...

In this work we present some exactness conditions for the Shor relaxation of diagonal (or, more generally, diagonalizable) QCQPs, which extend introduced in different recent papers about same topic. It is shown that equivalent to two convex quadratic relaxations. Then, sufficient relaxations are derived from their KKT systems. will be that, cases, by derivation previous literature, can viewed a...

By considering the epigraphs of conjugate functions, we extend the Fenchel duality, applicable to a (possibly infinite) family of proper lower semicontinuous convex functions on a Banach space. Applications are given in providing fuzzy KKT conditions for semi-infinite programming.

Two interior-point algorithms are proposed and analyzed, for the (local) solution of (possibly) indefinite quadratic programming problems. They are of the Newton-KKT variety in that (much like in the case of primal-dual algorithms for linear programming) search directions for the “primal” variables and the Karush-Kuhn-Tucker (KKT) multiplier estimates are components of the Newton (or quasi-Newt...