In this paper we study a class of Mayer-type hybrid optimal control problems. Using Lagrange techniques, we formulate a version of the Hybrid Maximum Principle for optimal control problems governed by hybrid systems with autonomous location transitions in the presence of additional target constraints.

The cones of directions of constancy are used to derive: new as well as known optimality conditions; weakest constraint qualifications; and regularization techniques, for the convex programming problem. In addition, the "badly behaved set" of constraints, i.e. the set of constraints which causes problems in the Kuhn-Tucker theory, is isolated and a computational procedure for checking whether a...

In this article, we study the existence of solution for the following elliptic system of variable exponents with perturbation terms − div |∇u|p(x)−2∇u) + |u|p(x)−2u = λa(x)|u|γ(x)−2u+ Fu(x, u, v) in R , − div |∇v|q(x)−2∇v) + |v|q(x)−2v = λb(x)|v|δ(x)−2v + Fv(x, u, v) in R , u ∈W 1,p(·)(RN ), v ∈W 1,q(·)(RN ), where the corresponding functional does not satisfy PS conditions. We obtain a suffici...

In this paper we discuss second-order properties of the Moreau-Yosida regularization F of a piecewise twice continuously differentiable convex function f . We introduce a new constraint qualification in order to prove that the gradient of F is piecewise continuously differentiable. In addition, we discuss conditions, depending on the Hessians of the pieces, that guarantee positive definiteness ...

The mechanical rolling conditions in hot strip mills are precisely defined by various variables, which are taken directly froth the rolling schedule (separation force, torque. speed. strip thickness) or calculated from figures of the rolling schedule and dimensions of the mill (strip reduction, roll diameter etc.). These variables allow to describe the mechanical rolling conditions of all passe...

Train energy saving problem investigates how to control train's velocity such that the quantity of energy consumption is minimized and some system constraints are satis ed. On the assumption that the train's weights on different links are estimated by fuzzy variables when making the train scheduling strategy, we study the fuzzy train energy saving problem. First, we propose a fuzzy energy ...

In this article, we discuss the sample average approximation (SAA) method applied to a class of stochastic mathematical programs with variational (equilibrium) constraints. To this end, we briefly investigate the structure of both – the lower level equilibrium solution and objective integrand. We show almost sure convergence of optimal values, optimal solutions (both local and global) and gener...

We study the Celis-Dennis-Tapia (CDT) problem: minimize a non-convex quadratic function over the intersection of two ellipsoids. In contrast to the well-studied trust region problem where the feasible set is just one ellipsoid, the CDT problem is not yet fully understood. Our main objective in this paper is to narrow the difficulty gap that occurs when the Hessian of the Lagrangian is indefinit...