Mathematical programs with vanishing constraints constitute a new class of difficult optimization problems with important applications in optimal topology design of mechanical structures. Vanishing constraints usually violate standard constraint qualifications, which gives rise to serious...

In this paper we investigate the relationship between the nearest point problem in a polyhedral cone and the nearest point problem in a polyhedral set, and use this relationship to devise an effective method for solving the latter using an existing algorithm for the former. We then show that...

For a general Markowitz portfolio selection problem with linear inequality constraints, it is not possible to obtain a closed form solution. The number of parametric intervals and corresponding segments of the efficient frontier is not known a priori. In this paper, we analyze the structure of...