in this paper, an efficient method for solving optimal control problemsof the linear differential systems with inequality constraint is proposed. by usingnew adjustment of hat basis functions and their operational matrices of integration,optimal control problem is reduced to an optimization problem. also, the erroranalysis of the proposed method is investigated and it is proved that the order o...

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

One often heard counter to the concern about rising income and wealth inequality is that it is wrong to focus on inequality of outcomes in a “snapshot”. Intergenerational mobility and “equality of opportunity”, so the argument goes, is what matters for normative evaluation. In response to this counter, we ask what pattern of intergenerational mobility leads to lower inequality not between indiv...

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and is shown to be the best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed and proved to be true in some significant special cases. Th...

Moreover we know exactly when the equality holds: if and only if D is a disc. For any optimal geometric inequality it is important to have a complete understanding of the equality case. Sometimes this can be easily achieved by checking the proof of the inequality. Take as an example the following elegant theorem due to Lichenerowicz [L]: let (M; g) be a compact Riemannian manifold of dimension ...

In this paper, a computational intelligence method is used for the solution of fractional optimal control problems (FOCP)'s with equality and inequality constraints. According to the Ponteryagin minimum principle (PMP) for FOCP with fractional derivative in the Riemann- Liouville sense and by constructing a suitable error function, we define an unconstrained minimization problem. In the optimiz...

international experiences reveal that promotion of gender equality paves the way for developmental achievements in a way that it ensures equal living standards and human rights for all individuals. nowadays gender equality is not only one of the principles of human rights but is emphasized for alleviating poverty, upgrading living standards and stabilizing economy. the relation between democrac...

We consider optimization problems with equality, inequality, and abstract set constraints. We investigate the relations between various characteristics of the constraint set related to the existence of Lagrange multipliers. For problems with no abstract set constraint, the classical condition of quasiregularity provides the connecting link between the most common constraint qualifications and e...

We consider the extended trust region subproblem (eTRS) as the minimization of an indefinite quadratic function subject to the intersection of unit ball with a single linear inequality constraint. Using a variation of the S-Lemma, we derive the necessary and sufficient optimality conditions for eTRS. Then, an OCP/SDP formulation is introduced for the problem. Finally, several illustrative examp...

A detailed investigation is undertaken into Brunn-Minkowski-type inequalities for Gauss measure. A Gaussian dual Brunn-Minkowski inequality, the first of its type, is proved, together with precise equality conditions, and shown to be best possible from several points of view. A new Gaussian Brunn-Minkowski inequality is proposed, and proved to be true in some significant special cases. Througho...