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1. STOCHASTIC SETUP-COST INVENTORY MODEL WITH BACKORDERS AND QUASICONVEX COST FUNCTIONS

   https://doi.org/10.1017/S0269964818000335  

   Feinberg, Eugene A.; Liang, Yan (April 2019, Probability in the Engineering and Informational Sciences)

   This paper studies a periodic-review single-commodity setup-cost inventory model with backorders and holding/backlog costs satisfying quasiconvexity assumptions. We show that the Markov decision process for this inventory model satisfies the assumptions that lead to the validity of optimality equations for discounted and average-cost problems and to the existence of optimal (s,S) policies. In particular, we prove the equicontinuity of the family of discounted value functions and the convergence of optimal discounted lower thresholds to the optimal average-cost lower threshold for some sequence of discount factors converging to 1. If an arbitrary nonnegative amount of inventory can be ordered, we establish stronger convergence properties: (i) the optimal discounted lower thresholds converge to optimal average-cost lower threshold; and (ii) the discounted relative value functions converge to average-cost relative value function. These convergence results previously were known only for subsequences of discount factors even for problems with convex holding/backlog costs. The results of this paper also hold for problems with fixed lead times. 

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2. Distributed Unconstrained Optimization with Time-varying Cost Functions

   https://doi.org/10.23919/ECC57647.2023.10178122  

   Esteki, Amir-Salar; Kia, Solmaz S. (June 2023, European Control Conference (ECC))

   This paper proposes a novel solution for the distributed unconstrained optimization problem where the total cost is the summation of time-varying local cost functions of a group networked agents. The objective is to track the optimal trajectory that minimizes the total cost at each time instant. Our approach consists of a two-stage dynamics, where the first one samples the first and second derivatives of the local costs periodically to construct an estimate of the descent direction towards the optimal trajectory, and the second one uses this estimate and a consensus term to drive local states towards the time-varying solution while reaching consensus. The first part is carried out by a weighted average consensus algorithm in the discrete-time framework and the second part is performed with a continuous-time dynamics. Using the Lyapunov stability analysis, an upper bound on the gradient of the total cost is obtained which is asymptotically reached. This bound is characterized by the properties of the local costs. To demonstrate the performance of the proposed method, a numerical example is conducted that studies tuning the algorithm’s parameters and their effects on the convergence of local states to the optimal trajectory. 

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3. Barren plateaus from learning scramblers with local cost functions

   https://doi.org/10.1007/JHEP01(2023)090  

   Garcia, Roy J.; Zhao, Chen; Bu, Kaifeng; Jaffe, Arthur (January 2023, Journal of High Energy Physics)

   A<sc>bstract</sc> The existence of barren plateaus has recently revealed new training challenges in quantum machine learning (QML). Uncovering the mechanisms behind barren plateaus is essential in understanding the scope of problems that QML can efficiently tackle. Barren plateaus have recently been shown to exist when learning global properties of random unitaries, which is relevant when learning black hole dynamics. Establishing whether local cost functions can circumvent these barren plateaus is pertinent if we hope to apply QML to quantum many-body systems. We prove a no-go theorem showing that local cost functions encounter barren plateaus in learning random unitary properties. 

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4. Predicting Performance and Cost of Serverless Computing Functions with SAAF

   https://doi.org/10.1109/DASC-PICom-CBDCom-CyberSciTech49142.2020.00111  

   Cordingly, Robert; Shu, Wen; Lloyd, Wes J. (August 2020, 2020 IEEE International Conference on Cloud and Big Data Computing)
5. Simplified Cost Functions Meet Advanced Muscle Models to Streamline Muscle Force Estimation

   https://doi.org/10.3390/biomed4030028  

   Ahmed, Muhammad Hassaan; N’Guessan, Jacques-Ezechiel; Das, Ranjan; Leineweber, Matthew; Goyal, Sachin (September 2024, BioMed)

   Background/Objectives: This study explores an optimization-based strategy for muscle force estimation by employing simplified cost functions integrated with physiologically relevant muscle models. Methods: Considering elbow flexion as a case study, we employ an inverse-dynamics approach to estimate muscle forces for the biceps brachii, brachialis, and brachioradialis, utilizing different combinations of cost functions and muscle constitutive models. Muscle force generation is modeled by accounting for active and passive contractile behavior to varying degrees using Hill-type models. In total, three separate cost functions (minimization of total muscle force, mechanical work, and muscle stress) are evaluated with each muscle force model to represent potential neuromuscular control strategies without relying on electromyography (EMG) data, thereby characterizing the interplay between muscle models and cost functions. Results: Among the evaluated models, the Hill-type muscle model that incorporates both active and passive properties, combined with the stress minimization cost function, provided the most accurate predictions of muscle activation and force production for all three arm flexor muscles. Our results, validated against existing biomechanical data, demonstrate that even simplified cost functions, when paired with detailed muscle models, can achieve high accuracy in predicting muscle forces. Conclusions: This approach offers a versatile, EMG-free alternative for estimating muscle recruitment and force production, providing a more accessible and adaptable tool for muscle force analysis. It has profound implications for enhancing rehabilitation protocols and athletic training, not only broadening the applicability of muscle force estimation in clinical and sports settings but also paving the way for future innovations in biomechanical research. 

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