Page 129 - IJOCTA-15-1

An International Journal of Optimization and Control: Theories & Applications
ISSN: 2146-0957 eISSN: 2146-5703
Vol.15, No.1, pp.123-136 (2025)
https://doi.org/10.36922/ijocta.1544

RESEARCH ARTICLE

Duality for robust multi-dimensional vector variational control
problem under invexity

1
1
Ritu Bagri , Geeta Sachdev , Divya Agarwal 2*
1 Department of Applied Sciences and Humanities, Indira Gandhi Delhi Technical University for Women,
Delhi, India
2 Amity Institute of Applied Sciences, Amity University Uttar Pradesh, India
ritu051phd21@igdtuw.ac.in, geetasachdev@igdtuw.ac.in, dagarwal1@amity.edu

ARTICLE INFO ABSTRACT

Article History: This paper presents a multi-dimensional vector variational control problem
Received: 10 February 2024 wherein constraints are comprised of first order partial derivatives. As the
Accepted: 4 January 2025 optimization problems may contain uncertainties driven by measurement and
Available Online: 27 January 2025 manufacturing errors, erroneous information, irregularities, or perturbations,
so the parameter’s randomness is assumed to be in the form of an uncertainty
Keywords:
set. Firstly, the sufficient efficiency conditions are demonstrated for the prob-
Duality theorems
lem under consideration. Then, the Wolfe type and Mond Weir type duals
Variational Control problem
of the primal problem have been formulated. As in multi objective optimiza-
Robust
tion models, attainment of efficient or weak efficient is the primary aim, thus
Multi-dimensional
the important robust duality theorems viz. weak, strong and strict converse
Invexity
duality theorems have been established under invexity conditions for Wolfe
AMS Classification 2010: type dual. An example is also provided to illustrate the weak duality theorem.
90C29; 90C46; 49N15 Thereafter, the duality results for Mond Weir type duals have been obtained
under weaker invexity assumptions on involved functionals. This work extends
the previously studied results on control problems and hence seeks application
in diverse fields.

1. Introduction data ambiguity. This phenomenon inspired re-
searchers to investigate several mathematical pro-
gramming problems in context of ambiguous data.
Multi-objective programming problems are 5
utilised to address and solve a variety of real- Beck and Ben-Tal demonstrated that the primal
world issues, such as those in engineering, pro- worst is equivalent to the dual best and arrived
at the robust optimization solution via duality.
duction planning, queueing and finance. For in- 6
1
stance, in the optimal cost and waiting time is Jeyakumar et al. established the robust dual-
ity results under data uncertainty for generalized
obtained by solving a bi-objective optimization 7
convex problems. Treant¸˘a and Das examined
problem for a queueing model. Significant ad-
curvilinear integral-based optimization problems
vancements in this field using the efficiency idea
can be seen in. 2–4 with robustness that have implications in mechan-
8
ical work. In, a new modified robust control
Uncertainty in the data is caused by lack of knowl- problem involving mixed constraints and second-
edge, out-of-date sources, large volume of data, order PDEs is explored.
sample inconsistency, etc., which creates a barrier In many branches of mathematics, economics, and
in pinpointing the precise solution to the prob- engineering sciences, multi-dimensional (multi-
lem. As a result, the robust technique is expand- time) control problems have been discovered as
ing quickly for solving problems where there is in. 9,10 Several authors have investigated control
*Corresponding Author
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