A barrier-type method for multiobjective optimization

For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary … Read more

An Interior-Point Method for Nonlinear Optimization Problems with Locatable and Separable Nonsmoothness

A lot of real-world optimization models comprise nonconvex and nonlinear as well as nonsmooth functions leading to very hard classes of optimization models. In this article a new interior-point method for the special but practically relevant class of optimization problems with locatable and separable nonsmooth aspects is presented. After motivating and formalizing the problems under … Read more

A local convergence property of primal-dual methods for nonlinear programming

We prove a new local convergence property of a primal-dual method for solving nonlinear optimization problem. Following a standard interior point approach, the complementarity conditions of the original primal-dual system are perturbed by a parameter which is driven to zero during the iterations. The sequence of iterates is generated by a linearization of the perturbed … Read more

An interior-point method for MPECs based on strictly feasible relaxations

An interior-point method for solving mathematical programs with equilibrium constraints (MPECs) is proposed. At each iteration of the algorithm, a single primal-dual step is computed from each subproblem of a sequence. Each subproblem is defined as a relaxation of the MPEC with a nonempty strictly feasible region. In contrast to previous approaches, the proposed relaxation … Read more

Assessing the Potential of Interior Methods for Nonlinear Optimization

A series of numerical experiments with interior point (LOQO, KNITRO) and active-set SQP codes (SNOPT, filterSQP) are reported and analyzed. The tests were performed with small, medium-size and moderately large problems, and are examined by problem classes. Detailed observations on the performance of the codes, and several suggestions on how to improve them are presented. … Read more