This paper presents a new clustering algorithm ,which is based on fuzzy c-lines, can treat data with some errors. First, the tolerance is formulated and introduce into optimization problem of clustering. Next, the problem is solved using Karush-Kuhn-Tucker conditions. Last, the algorithm is constructed based on the results of solving the problem. Some numerical examples for the proposed method ...

We study the problem of solving a constrained system of nonlinear equations by a combination of the classical damped Newton method for (unconstrained) smooth equations and the recent interior point potential reduction methods for linear programs, linear and nonlin-ear complementarity problems. In general, constrained equations provide a uniied formulation for many mathematical programming probl...

Abs t rac t -P roper t i e s of nonlinear multiobjective problems implied by the Karush-Kuhn-Tucker necessary conditions are investigated. It is shown that trajectories of Lagrange multipliers corresponding to the components of the vector cost function are orthogonal to the corresponding trajectories of vector deviations in the balance space (to the balance set for Pareto solutions). ~) 2003 El...

In the context of mixed complementarity problems, various concepts of solution regularity are known, each of them playing a certain role in related theoretical and algorithmic developments. In this note, we provide the complete picture of relations between the most important regularity conditions for mixed complementarity problems. A special attention is paid to the particular cases of a nonlin...

We propose to solve a general quasi-variational inequality by using its Karush-Kuhn-Tucker conditions. To this end we use a globally convergent algorithm based on a potential reduction approach. We establish global convergence results for many interesting instances of quasi-variational inequalities, vastly broadening the class of problems that can be solved with theoretical guarantees. Our nume...

In this paper, we propose a new method for solving large-scale ill-posed problems. This method is based on the Karush–Kuhn–Tucker conditions, Fisher–Burmeister function and the discrepancy principle. The main difference from the majority of existing methods for solving ill-posed problems is that, we do not need to choose a regularization parameter in advance. Experimental results show that the ...

This paper studies bilevel polynomial optimization. We propose a method to solve it globally by using optimization relaxations. Each relaxation is obtained from the Karush--Kuhn--Tucker ...

We consider rules for discarding predictors in lasso regression and related problems, for computational efficiency. El Ghaoui and his colleagues have propose 'SAFE' rules, based on univariate inner products between each predictor and the outcome, which guarantee that a coefficient will be 0 in the solution vector. This provides a reduction in the number of variables that need to be entered into...

In this paper, we are concerned with a fractional multiobjective optimization problem ( P ). Using support functions together generalized Guignard constraint qualification, give necessary optimality conditions in terms of convexificators and the Karush–Kuhn–Tucker multipliers. Several intermediate problems have been introduced to help us our investigation.