Generic Existence of Solutions of Nonconvex Optimal Control Problems
نویسنده
چکیده
The Tonelli existence theorem in the calculus of variations and its subsequent modifications were established for integrands f which satisfy convexity and growth conditions. In 1996, the author obtained a generic existence and uniqueness result (with respect to variations of the integrand of the integral functional) without the convexity condition for a class of optimal control problems satisfying the Cesari growth condition. In this paper, we survey this result and its recent extensions, and establish several new results in this direction.
منابع مشابه
Optimality conditions for approximate solutions of vector optimization problems with variable ordering structures
We consider nonconvex vector optimization problems with variable ordering structures in Banach spaces. Under certain boundedness and continuity properties we present necessary conditions for approximate solutions of these problems. Using a generic approach to subdifferentials we derive necessary conditions for approximate minimizers and approximately minimal solutions of vector optimizatio...
متن کاملExistence of Solutions for a Class of Infinite Horizon Optimal Control Problems without Discounting Arising in Economic Dynamics
The study of the existence and the structure of solutions of optimal control problems defined on infinite intervals and on sufficiently large intervals has recently become a rapidly growing area of research. See, for example, [2], [4]-[9], [13, 14,17,18], [22]-[26], [30] and the references mentioned therein. These problems arise in engineering [1,12,15], in models of economic growth [11,19,21,2...
متن کاملAn Efficient Neurodynamic Scheme for Solving a Class of Nonconvex Nonlinear Optimization Problems
By p-power (or partial p-power) transformation, the Lagrangian function in nonconvex optimization problem becomes locally convex. In this paper, we present a neural network based on an NCP function for solving the nonconvex optimization problem. An important feature of this neural network is the one-to-one correspondence between its equilibria and KKT points of the nonconvex optimizatio...
متن کاملA numerical method for nonconvex multi-objective optimal control problems
A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obt...
متن کاملA semidefinite relaxation scheme for quadratically constrained
Semidefinite optimization relaxations are among the widely used approaches to find global optimal or approximate solutions for many nonconvex problems. Here, we consider a specific quadratically constrained quadratic problem with an additional linear constraint. We prove that under certain conditions the semidefinite relaxation approach enables us to find a global optimal solution of the unde...
متن کامل