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Abstract:
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The continuous-time programming problem consists in minimizing an integral functional, with
phase constraints of different types.
The subject of this doctoral dissertation is to establish extremum conditions as well as
duality theorems for a class of convex and smooth continuous-time programming problems,
with phase constraints of the inequality type. Unfortunately, some of the results in this field
are not valid, which is confirmed in 2019.
In this paper, new optimality conditions for the aforementioned class of problems are ob tained. The theorems of weak and strong duality are proved. The main tool for deriving these
results is a new theorem of the alternative for a convex system of strict and nonstrict inequal ities in infinite dimensional spaces. In order to apply the aforementioned theorem, a suitable
regularity condition must be satisfied. Some optimality conditions are obtained with additional
constraint regularity qualification. Theoretical results are confirmed by practical examples. |