Civic Crowdfunding (CC) uses the ``power of crowd" to garner contributions towards public projects. As these projects are non-excludable, agents may prefer ``free-ride," resulting in project not being funded. Researchers introduce refunds for single CC incentivize contribute, guaranteeing project's funding. These funding guarantees applicable only when have an unlimited budget. This paper focus...

For optimal control problems involving ordinary differential equations and functional inequality state constraints, the maximum principle may degenerate, producing no useful information about minimizers. This is known as the degeneracy phenomenon. Several non-degenerate forms of the maximum principle, valid under different constraint qualifications, have been proposed in the literature. In this...

In this contribution, we consider a class of hybrid systems with continuous dynamics and jumps in the continuous state (impulsive hybrid systems). By using a newly elaborated version of the Pontryagintype Maximum Principle (MP) for optimal control processes governed by hybrid dynamics with autonomous location transitions, we extend the necessary optimality conditions to a class of Impulsive Hyb...

The aim of this article is to study an optimal control problem for a system of nonlinear elliptic equations with Dirichlet boundary conditions, u x a x x c x u x eu x u x x , Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . x , 1.1 Ž . x b x u x d x x f x u x x , Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . Ž . x , u x x 0, on , Ž . Ž . 1, 2 The authors were supported in part by CICYT, Ministry of Education and Culture,...

This paper shows how to construct and implement explicit MPC feedback laws for systems with a large number of states. Specifically, the construction of critical regions of the explicit MPC solution is replaced by a two-step procedure. First, all optimal active sets are enumerated off-line and corresponding KKT matrices are pre-factored. Then, in the on-line step, the optimal control inputs are ...

For some optimal control problems with pathwise state constraints the standard versions of the necessary conditions of optimality are unable to provide useful information to select minimizers. There exist some literature on stronger forms of the maximum principle, the so-called nondegenerate necessary conditions, that can be informative for those problems. These conditions can be applied when c...

A class of parametric optimal control problems for semilinear parabolic equations is considered. Using recent regularity results for solutions of such equations, suucient conditions are derived under which the solutions to optimal control problems are locally Lipschitz continuous functions of the parameter in the L 1-norm. It is shown that these conditions are also necessary, provided that the ...

An optimal control problem is studied for a predator-prey reaction-diffusion system. A hunter population is introduced in the ecosystem and it is interpreted as a control variable. One finds necessary optimality conditions in order that, in the end of a given time interval, the total density of the two populations is maximal.

In this paper we consider a elastic vector-valued Allen-Cahn MPCC (Mathematical Programs with Complementarity Constraints) problem. We use a regularization approach to get the optimality system for the subproblems. By passing to the limit in the optimality conditions for the regularized subproblems, we derive certain generalized first-order necessary optimality conditions for the original problem.

The paper revisits the issue of necessary optimality conditions for infinite-horizon optimal control problems. It is proved that the normal form maximum principle holds with an explicitly specified adjoint variable if an appropriate relation between the discount rate, the growth rate of the solution and the growth rate of the objective function is satisfied. The main novelty is that the result ...