In this note the Hamiltonian cycle problem is mapped into an infinite horizon discounted cost constrained Markov decision problem. The occupation measure based linear polytope associated with this control problem defines a convex set which either strictly contains or is equal to another convex...

We introduce the time-consistency concept that is inspired by the so-called “principle of optimality” of dynamic programming and demonstrate – via an example – that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of...

We consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$$\varepsilon.$$</EquationSource> </InlineEquation> We study the behaviour of the solutions of such a perturbed problem as <InlineEquation ID="IEq1"> <EquationSource...</equationsource></inlineequation></equationsource></inlineequation>

We introduce the time-consistency concept that is inspired by the so-called “principle of optimality” of dynamic programming and demonstrate – via an example – that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of...

We consider a perturbed mathematical programming problem where both the objective and the constraint functions are polynomial in all underlying decision variables and in the perturbation parameter $$\varepsilon.$$ We study the behaviour of the solutions of such a perturbed problem as...