On Some Constrained Optimization Problems

On Resource Constrained Optimization Problems

This paper shows that a method that has long been used to solve Resource Constrained Optimization Problems and found extremely effective in practice, is effective in the theoretical sense as well, it is proved to be strongly polynomial. In the special case of Resource Constrained Shortest Path Problem a better running time estimation is also presented.

Equilibrium constrained optimization problems

We consider equilibrium constrained optimization problems, which have a general formulation that encompasses well-known models such as mathematical programs with equilibrium constraints, bilevel programs, and generalized semi-infinite programming problems. Based on the celebrated KKM lemma, we prove the existence of feasible points for the equilibrium constraints. Moreover, we analyze the topol...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

On Some Rescaled Shape Optimization Problems

We consider Cheeger-like shape optimization problems of the form min { |Ω|J(Ω) : Ω ⊂ D } where D is a given bounded domain and α is above the natural scaling. We show the existence of a solution and analyze as J(Ω) the particular cases of the compliance functional C(Ω) and of the first eigenvalue λ1(Ω) of the Dirichlet Laplacian. We prove that optimal sets are open and we obtain some necessary ...

Some Global Optimization Problems on Stiefel Manifolds

Optimization on Stiefel manifolds was discussed by Rapcsák in earlier papers, and some global optimization methods were considered and tested on Stiefel manifolds. In the paper, test functions are given with known global optimum points and their optimal function values. A restriction, which leads to a discretization of the problem is suggested, which results in a problem equivalent to the well-...