arXiv subjects

Sina Kazemdehbashi

Publications and source records attributed to Sina Kazemdehbashi.

5 recordsLinked to original sources

arXiv2026

Nonmonotone Coderivative-Based Newton Methods for Nonsmooth Optimization with Machine Learning Applications

Newton-type algorithms are among the most effective methods for solving optimization problems because of their rapid local convergence. However, extending these methods to nonsmooth optimization is challenging due to the difficulty of incorporating second-order information. To address this issue, we propose a coderivative-based Newton framework for solving both unconstrained and constrained nonsmooth optimization problems using tools from variational analysis and generalized differentiation. The proposed method employs generalized Hessians, defined as coderivatives of the subgradient mapping, and is applicable to both $C ^{1,1}$ functions and convex composite optimization problems with extended-real-valued components. To enhance robustness, the algorithm incorporates an adaptive regularization strategy that enables it to handle problems whose generalized Hessians are positive semidefinite. In addition, a Hybrid Adaptive Nonmonotone (HAN) line search scheme is developed as a globalization technique to improve global convergence and practical performance. Under standard assumptions, both the exact and inexact versions of the algorithm are globally convergent and achieve local superlinear convergence when the associated subgradient mapping satisfies the semismooth* property. The proposed framework is further extended to convex composite optimization through the forward-backward envelope, allowing it to handle problems with or without strong convexity in the smooth component of the objective function. Numerical experiments on Lasso, logistic Lasso, and support vector machine (SVM) problems demonstrate the efficiency and robustness of the proposed algorithm. Comparisons with several well-established first-order and second-order methods for nonsmooth optimization show that the proposed approach is computationally competitive while maintaining strong convergence properties.

math.OC↗

arXiv2026

Trend-Adjusted Time Series Models with an Application to Gold Price Forecasting

Time series data play a critical role in various fields, including finance, healthcare, marketing, and engineering. A wide range of techniques (from classical statistical models to neural network-based approaches such as Long Short-Term Memory (LSTM)) have been employed to address time series forecasting challenges. In this paper, we reframe time series forecasting as a two-part task: (1) predicting the trend (directional movement) of the time series at the next time step, and (2) forecasting the quantitative value at the next time step. The trend can be predicted using a binary classifier, while quantitative values can be forecasted using models such as LSTM and Bidirectional Long Short-Term Memory (Bi-LSTM). Building on this reframing, we propose the Trend-Adjusted Time Series (TATS) model, which adjusts the forecasted values based on the predicted trend provided by the binary classifier. We validate the proposed approach through both theoretical analysis and empirical evaluation. The TATS model is applied to a volatile financial time series (the daily gold price) with the objective of forecasting the next days price. Experimental results demonstrate that TATS consistently outperforms standard LSTM and Bi-LSTM models by achieving significantly lower forecasting error. In addition, our results indicate that commonly used metrics such as MSE and MAE are insufficient for fully assessing time series model performance. Therefore, we also incorporate trend detection accuracy, which measures how effectively a model captures trends in a time series.

cs.LG↗

arXiv2025

New Location Science Models with Applications to UAV-Based Disaster Relief

Natural and human-made disasters can cause severe devastation and claim thousands of lives worldwide. Therefore, developing efficient methods for disaster response and management is a critical task for relief teams. One of the most essential components of effective response is the rapid collection of information about affected areas, damages, and victims. More data translates into better coordination, faster rescue operations, and ultimately, more lives saved. However, in some disasters, such as earthquakes, the communication infrastructure is often partially or completely destroyed, making it extremely difficult for victims to send distress signals and for rescue teams to locate and assist them in time. Unmanned Aerial Vehicles (UAVs) have emerged as valuable tools in such scenarios. In particular, a fleet of UAVs can be dispatched from a mobile station to the affected area to facilitate data collection and establish temporary communication networks. Nevertheless, real-world deployment of UAVs faces several challenges, with adverse weather conditions--especially wind--being among the most significant. To address this, we develop a novel mathematical framework to determine the optimal location of a mobile UAV station while explicitly accounting for the heterogeneity of the UAVs and the effect of wind. In particular, we generalize the Sylvester problem to introduce the Sylvester-Fermat-Torricelli (SFT) problem, which captures complex factors such as wind influence, UAV heterogeneity, and back-and-forth motion within a unified framework. The proposed framework enhances the practicality of UAV-based disaster response planning by accounting for real-world factors such as wind and UAV heterogeneity. Experimental results demonstrate that it can reduce wasted operational time by up to 84%, making post-disaster missions significantly more efficient and effective.

cs.RO↗

arXiv2024

Adaptive grid-based decomposition for UAV-based coverage path planning in maritime search and rescue

Unmanned aerial vehicles (UAVs) are increasingly utilized in search and rescue (SAR) operations to enhance efficiency by enabling rescue teams to cover large search areas in a shorter time. Reducing coverage time directly increases the likelihood of finding the target quickly, thereby improving the chances of a successful SAR operation. In this context, UAVs require path planning to determine the optimal flight path that fully covers the search area in the least amount of time. A common approach involves decomposing the search area into a grid, where the UAV must visit all cells to achieve complete coverage. In this paper, we propose an Adaptive Grid-based Decomposition (AGD) algorithm that efficiently partitions polygonal search areas into grids with fewer cells. Additionally, we utilize a Mixed-Integer Programming (MIP) model, compatible with the AGD algorithm, to determine a flight path that ensures complete cell coverage while minimizing overall coverage time. Experimental results highlight the efficiency of the AGD algorithm in reducing coverage time (by up to 20%) across various scenarios.

cs.RO↗

arXiv2024

An exact coverage path planning algorithm for UAV-based search and rescue operations

Unmanned aerial vehicles (UAVs) are increasingly utilized in global search and rescue efforts, enhancing operational efficiency. In these missions, a coordinated swarm of UAVs is deployed to efficiently cover expansive areas by capturing and analyzing aerial imagery and footage. Rapid coverage is paramount in these scenarios, as swift discovery can mean the difference between life and death for those in peril. This paper focuses on optimizing flight path planning for multiple UAVs in windy conditions to efficiently cover rectangular search areas in minimal time. We address this challenge by dividing the search area into a grid network and formulating it as a mixed-integer program (MIP). Our research introduces a precise lower bound for the objective function and an exact algorithm capable of finding either the optimal solution or a near-optimal solution with a constant absolute gap to optimality. Notably, as the problem complexity increases, our solution exhibits a diminishing relative optimality gap while maintaining negligible computational costs compared to the MIP approach.

cs.RO↗