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@article{168332,
        author = {ANIL KUMAR},
        title = {Online Convex Optimization for NP-Hard Problems},
        journal = {International Journal of Innovative Research in Technology},
        year = {2024},
        volume = {11},
        number = {5},
        pages = {404-410},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=168332},
        abstract = {Online Convex Optimization (OCO) provides a powerful framework for addressing dynamic decision-making processes in environments where data arrives sequentially. Although NP-hard problems are inherently challenging due to their computational complexity, OCO offers an efficient, approximate solution technique that adapts to real-time data and constraints. In the OCO framework, decisions are made incrementally without full knowledge of future inputs, with the goal of minimizing a loss function over time. By leveraging convexity properties and optimization techniques, OCO can approximate solutions to NP-hard problems such as online linear programming, scheduling, resource allocation, and sub modular maximization. This approach is particularly effective in scenarios like machine learning, network optimization, and online markets, where decisions must be made iteratively under uncertainty. OCO allows for real-time adjustments based on immediate feedback, often with competitive guarantees that bound the difference between online solutions and offline optimal outcomes. Through methods such as gradient descent, mirror descent, and regret minimization, OCO facilitates scalable and practical approximations for NP-hard problems that otherwise resist tractable solutions in static, offline settings. Thus, online convex optimization extends traditional optimization methods, making it a critical tool in solving complex, real-time NP-hard problems across various industries, including finance, logistics, and telecommunications.},
        keywords = {NP-Hard Problems, Dynamic Decision-Making, Real-Time optimization, Gradient Descent, Mirror Descent, Regret Minimization, Sub modular maximization, Sequential Decision-Making, Online Learning},
        month = {October},
        }