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The goal of this paper is to derive some error estimates for the
numerical discretization of some optimal control problems governed
by semilinear elliptic equations with bound constraints on the
control and a finitely number of equality and inequality state
constraints. We prove some error estimates for the optimal
controls in the L∞ norm and we also obtain error estimates
for the Lagrange multipliers associated to the state constraints
as well as for the optimal states and optimal adjoint states.
...
In this paper, a distributed optimal consensus problem is investigated to achieve the optimization of the sum of local cost function for a group of agents in the Euler-Lagrangian (EL) system form. We consider that the local cost function of each agent is only known by itself and cannot be shared with others, which brings challenges in this distributed optimization problem. A novel gradient-based distributed continuous-time algorithm with the parameters of EL system is proposed, which takes the distributed...
The criteria of extremality for classical variational integrals depending on several functions of one independent variable and their derivatives of arbitrary orders for constrained, isoperimetrical, degenerate, degenerate constrained, and so on, cases are investigated by means of adapted Poincare-Cartan forms. Without ambitions on a noble generalizing theory, the main part of the article consists of simple illustrative examples within a somewhat naive point of view in order to obtain results resembling...
Continuing the previous Part I, the degenerate first order variational integrals depending on two functions of one independent variable are investigated.
We will deal with a new geometrical interpretation of the classical Legendre and Jacobi conditions: they are represented by the rate and the magnitude of rotation of certain linear subspaces of the tangent space around the tangents to the extremals. (The linear subspaces can be replaced by conical subsets of the tangent space.) This interpretation can be carried over to nondegenerate Lagrange problems but applies also to the degenerate variational integrals mentioned in the preceding Part II.
Variational integrals containing several functions of one independent variable subjected moreover to an underdetermined system of ordinary differential equations (the Lagrange problem) are investigated within a survey of examples. More systematical discussion of two crucial examples from Part I with help of the methods of Parts II and III is performed not excluding certain instructive subcases to manifest the significant role of generalized Poincaré-Cartan forms without undetermined multipliers....
In this paper, which is an extension of [4],
we first show the existence of solutions to
a class of Min Sup problems with
linked constraints, which satisfy a certain property. Then, we apply our result to a class of weak nonlinear bilevel
problems. Furthermore, for such a class of bilevel problems, we
give a relationship with appropriate d.c. problems concerning the
existence of solutions.
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