Computing meaningful alternative routes in a road network is a complex problem – already giving a clear definition of a best alternative seems to be impossible. Still, multiple methods [1, 2, 4, 17, 18] describe how to compute reasonable alternative routes, each according to their own quality criteria. Among these methods, the penalty method has received much less attention than the via-node or...

This note considers possible arrangements of the sectors of a generalised dartboard. The sum of the pth powers of the absolute differences of the numbers on adjacent sectors is introduced as a penalty cost function and a string reversal algorithm is used to determine all arrangements that maximise the penalty, for any p ≥ 1. The maximum value of the penalty function for p = 1 is well known in t...

it has been revealed that the surface stress effect plays an important role in the mechanical behavior ofstructures (such as bending, buckling and vibration) when their dimensions are on the order ofnanometer. in addition, recent advances in nanotechnology have proposed several applications fornanoscale shells in different fields. hence, in the present article, within the framework of surfaceel...

A new projective exact penalty function method is proposed for the equivalent reduction of constrained optimization problems to unconstrained ones. In method, original objective extended infeasible points by summing its value at projection an point on feasible set with distance set. The equivalence means that local and global minimums coincide. Nonconvex sets multivalued projections are admitte...

In this paper, we give a sufficient condition for the asymptotic convergence of penalty trajectories in convex programming with multiple solutions. We show that, for a wide class of penalty methods, the associated optimal trajectory converges to a particular solution of the original problem, characterized through a minimization selection principle. Our main assumption for this convergence resul...