We propose an extension of the classical real-valued external penalty method to the multicriteria optimization setting. As its single objective counterpart, it also requires an external penalty function for the constraint set, as well as an exogenous divergent sequence of nonnegative real numbers, the so-called penalty parameters, but, differently from the scalar procedure, the vector-valued me...

We shall first briefly review our results related to solving of the convex box constrained quadratic programming problems by combination of the active set strategy and the conjugate gradient method with projections [1]. In particular, we shall show that with proper modification of the proportioning algorithm with projection [2], it is possible give the rate of convergence in terms of the spectr...

In this paper, we considered the role of penalty when the higher-order conjugate gradient method (HCGM) was used as a computational scheme for the minimization of penalised cost functions for optimal control problems described by linear systems and integral quadratic costs. For this family of commonly encountered problems, we find out that the conventional penalty methods require very large pen...

This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling salesman problem with time windows (TSPTW). Augmenting temperature from traditional simulated annealing with the concept of pressure (analogous to the value of the penalty multiplier), compressed annealing relaxes the time window constraints by integrating a penalty method within...

In this paper, first the validity of 3-D DDA is examined by comparing its solution for dynamic block displacement with analytical solution. Displacement of a single block on an inclined plane subjected to a dynamic loading is studied for analytical solution with respect to the frictional resistance offered by the inclined slope. 3-D DDA predicts accurately the analytical displacements. The modi...

1. Abstract In traditional structural topology optimization (TO), the material properties of continuum finite elements of fixed form and coupling are varied to find the optimal topology that satisfies the design problem. We develop an alternative, fundamental formulation where the design space search is dependent on the coupling, and the goal of the topology optimization by penalty (TOP) method...

This paper describes a variant of simulated annealing incorporating a variable penalty method to solve the traveling salesman problem with time windows (TSPTW). Augmenting temperature from traditional simulated annealing with the concept of pressure (analogous to the value of the penalty multiplier), compressed annealing integrates a penalty method with heuristic search to address the TSPTW. Co...

This paper, concluding the trilogy, develops schemes for the stable solution of wave-dominated unsteady problems in general three-dimensional domains. The schemes utilize a spectral approximation in each sub-domain and asymptotic stability of the semi-discrete schemes is established. The complex computational domains are constructed by using non-overlapping quadrilaterals in the two-dimensional...

A variable V-cycle preconditioner for an interior penalty finite element discretization for elliptic problems is presented. An analysis under a mild regularity assumption shows that the preconditioner is uniform. The interior penalty method is then combined with a discontinuous Galerkin scheme to arrive at a discretization scheme for an advection-diffusion problem, for which an error estimate i...

The penalty method is a method to generate alternative solutions for many discrete optimization problems. A penalty parameter easily allows to have influence on the difference between optimal and alternative solution. We experimentally test the penalty method for three optimization problems (shortest paths, assignments, travelling salesman) with parameters that change between planning phase and...