Foreword

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45206/1/10957_2004_Article_BF00934047.pd

Foreword

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45198/1/10957_2004_Article_BF00933202.pd

Geometric and analytic views in existence theorems for optimal control in Banach spaces. Part 1. Distributed parameters

Existence theorems for optimal control problems in Banach spaces are stated and proved.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45196/1/10957_2004_Article_BF00932845.pd

An elementary proof of an equivalence theorem relevant in the theory of optimization

A corrigendum in Ref. 1 is given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45224/1/10957_2004_Article_BF00940679.pd

Existence theorems for nonselfadjoint semilinear elliptic boundary value problems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25525/1/0000066.pd

On recent existence theorems in the theory of optimization

A condition recently proposed is shown to imply the weak compactness in H 1,1 and actually is equivalent to another condition previously proposed by the authors. Once compactness is proved, then existence theorems follow from lower closure theorems also previously proved by the authors, and extended to Pareto problems. The present analysis adds to the recent work of Goodman concerning the equivalence of seminormality conditions with concepts of convex analysis and lattice theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45217/1/10957_2004_Article_BF01262981.pd

Existence of solutions to nonselfadjoint boundary value problems for ordinary differential equations

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25524/1/0000065.pd

Nemitsky's operators and lower closure theorems

This paper focuses on certain analytic criteria given by the authors in earlier works, for the geometric property of upper semicontinuity of set-valued functions, used in the proofs of lower closure theorems, and hence in existence theory. In particular, it is observed that, under Filippov-type condition (namely, when the set of controls is bounded in measure or in norm), mere Carathéodory-type continuity of the relevant functions f is sufficient to guarantee a weak form of property (Q), and in turn the lower closure theorems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45208/1/10957_2004_Article_BF00934059.pd

Existence theorems for abstract multidimensional control problems

In the present paper, the author discusses an abstract formulation of control problems involving general operators ℒ : S → V , ℳ : S → Y from a Banach space S into space V and Y of vector functions in a fixed domain with components in L p , p ⩾1. For this general formulation, the author states closure theorems, lower closure theorems, and existence theorems for an optimal solution. It is then shown that the problems of control involving Dieudonné-Rashevski partial differential equations previously considered by the author are particular cases of the present formulation. Finally, it is shown by examples that problems of control involving usual partial differential equations, linear or not, as well as other functional relations, can be framed in the present formulation. The present work concerns problems with distributed controls . Work concerning problems with distributed as well as boundary controls is forthcoming.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45235/1/10957_2004_Article_BF00926601.pd