In this paper we consider nonlinear constrained optimization problems in case where the first order derivatives of the objective function and the constraints can not be used. Up to date only a few approaches have been proposed for tackling such a class of problems. In this work we propose a new algorithm. The starting point of the proposed approach is the possibility to transform the original c...

In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact l1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were ...

In signal processing, high resolution signal parameter estimation is a significant problem. In particular the estimation of the direction of the narrow band signals emitted by multiple sources received wide applications recently in signal processing literature. Quite a number of papers appeared in the last twenty five years regarding the estimation of the parameters of the direction of arrival ...

KEYWORDS In this paper, we consider scheduling of project networks under minimization of total weighted resource tardiness penalty costs. In this problem, we assume constrained resources are renewable and limited to very costly machines and tools which are also used in other projects and are not accessible in all periods of time of a project. In other words, there is a dictated ready date as we...

In sparse Bayesian learning (SBL), Gaussian scale mixtures (GSMs) have been used to model sparsity-inducing priors that realize a class of concave penalty functions for the regression task in real-valued signal models. Motivated by the relative scarcity of formal tools for SBL in complex-valued models, this paper proposes a GSM model the Bessel K model that induces concave penalty functions for...

Constrained optimization is a computationally difficult task, particularly if the constraint functions are non-linear and nonconvex. As a generic classical approach, the penalty function approach is a popular methodology which degrades the objective function value by adding a penalty proportional to the constraint violation. However, the penalty function approach has been criticized for its sen...

We consider the following classes of nonlinear programming problems: the minimization of smooth functions subject to general constraints and simple bounds on the variables; the noniinear l~problem; and the minimax problem. Numerically reliable methods for solving problems in each of these classes, based upon exploiting the structure of the problem in constructing simple differentiable penalty f...

In this paper we consider inequality constrained nonlinear optimization problems where the first order derivatives of the objective function and the constraints cannot be used. Our starting point is the possibility to transform the original constrained problem into an unconstrained or linearly constrained minimization of a nonsmooth exact penalty function. This approach shows two main difficult...