This study proposes a mathematical programming-based algorithm for the integrated selection of variable subsets and bandwidth estimation in geographically weighted regression, a local regression method that allows the kernel bandwidth and regression coefficients to vary across study areas. Unlike standard approaches in the literature, in which bandwidth and regression parameters are estimated separately for each focal point on the basis of different criteria, our model uses a single objective function for the integrated estimation of regression and bandwidth parameters across all focal points, based on the regression likelihood function and variance modeling. The proposed model further integrates a procedure to select a single subset of independent variables for all focal points, whereas existing approaches may return heterogeneous subsets across focal points. We then propose an alternative direction method to solve the nonconvex mathematical model and show that it converges to a partial minimum. The computational experiment indicates that the proposed algorithm provides competitive explanatory power with stable spatially varying patterns, with the ability to select the best subset and account for additional constraints.

In conceptual aircraft design, the problem of shaping a typical wing is usually decomposed into two parts: planform design and airfoil design. The latter, which is the focus of this work, is a multidisciplinary design problem that requires consideration of a variety of aerodynamic, structural, and manufacturing objectives and constraints. A non-exhaustive list of major considerations could include: Profile drag across the expected operating range of the airfoil (spanning lift coefficients, Reynolds numbers, and Mach numbers), including adequate off-design performance [1]; Pitching moment and aft-camber coefficients, which can drive tail sizing (modifying trim drag), affect divergence speed; Hinge moments and control effectiveness of any control surfaces, which drive actuator design and weight; Stall behavior, which can affect handling qualities and safety; Thickness at various points, in order to accommodate fuel volume and required structural members to resist failure (e.g., by bending, buckling, divergence, flutter, or control reversal);[2] Sensitivity to boundary layer performance, freestream turbulence, and trips, all of which impose constraints on surface finish, cleanliness, and manufacturing tolerances [3-5]; Peak suction pressures, which affect the critical Mach number in transonic applications or cavitation in hydrodynamic applications; Shock stability and buffet considerations in transonic applications; Manufacturability, which might include flat-bottom airfoil sections, strictly-convex airfoil shapes (e.g., to

Federated Learning (FL) enables privacy-preserving multi-source information fusion (MSIF) but is challenged by client drift in highly heterogeneous data settings. Many existing drift-mitigation strategies rely on reference-based techniques--such as gradient adjustments or proximal loss--that use historical snapshots (e.g., past gradients or previous global models) as reference points. When only a subset of clients participates in each training round, these historical references may not accurately capture the overall data distribution, leading to unstable training. In contrast, our proposed Gradient Centralized Federated Learning (GC-Fed) employs a hyperplane as a historically independent reference point to guide local training and enhance inter-client alignment. GC-Fed comprises two complementary components: Local GC, which centralizes gradients during local training, and Global GC, which centralizes updates during server aggregation. In our hybrid design, Local GC is applied to feature-extraction layers to harmonize client contributions, while Global GC refines classifier layers to stabilize round-wise performance. Theoretical analysis and extensive experiments on benchmark FL tasks demonstrate that GC-Fed effectively mitigates client drift and achieves up to a 20% improvement in accuracy under heterogeneous and partial participation conditions.

Domain-Independent Dynamic Programming (DIDP) is a state-space search paradigm based on dynamic programming for combinatorial optimization. In its current implementation, DIDP guides the search using user-defined dual bounds. Reinforcement learning (RL) is increasingly being applied to combinatorial optimization problems and shares several key structures with DP, being represented by the Bellman equation and state-based transition systems. We propose using reinforcement learning to obtain a heuristic function to guide the search in DIDP. We develop two RL-based guidance approaches: value-based guidance using Deep Q-Networks and policy-based guidance using Proximal Policy Optimization. Our experiments indicate that RL-based guidance significantly outperforms standard DIDP and problem-specific greedy heuristics with the same number of node expansions. Further, despite longer node evaluation times, RL guidance achieves better run-time performance than standard DIDP on three of four benchmark domains.

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting where the optimization problems to be solved change over time as new measurements are taken, and we establish linear convergence results for both the best and Polyak step sizes after a burn-in period. Additionally, we characterize the asymptotic convergence of the best average sub-optimality gap under diminishing and constant step sizes. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth objectives.

In this paper we propose and investigate a wide class of Mirror Descent updates (MD) and associated novel Generalized Exponentiated Gradient (GEG) algorithms by exploiting various trace-form entropies and associated deformed logarithms and their inverses - deformed (generalized) exponential functions. The proposed algorithms can be considered as extension of entropic MD and generalization of multiplicative updates. In the literature, there exist nowadays over fifty mathematically well defined generalized entropies, so impossible to exploit all of them in one research paper. So we focus on a few selected most popular entropies and associated logarithms like the Tsallis, Kaniadakis and Sharma-Taneja-Mittal and some of their extension like Tempesta or Kaniadakis-Scarfone entropies. The shape and properties of the deformed logarithms and their inverses are tuned by one or more hyperparameters. By learning these hyperparameters, we can adapt to distribution of training data, which can be designed to the specific geometry of the optimization problem, leading to potentially faster convergence and better performance. The using generalized entropies and associated deformed logarithms in the Bregman divergence, used as a regularization term, provides some new insight into exponentiated gradient descent updates.

Wind power producers (WPPs) participating in short-term power markets face significant imbalance costs due to their non-dispatchable and variable production. While some WPPs have a large enough market share to influence prices with their bidding decisions, existing optimal bidding methods rarely account for this aspect. Price-maker approaches typically model bidding as a bilevel optimization problem, but these methods require complex market models, estimating other participants' actions, and are computationally demanding. To address these challenges, we propose an online learning algorithm that leverages contextual information to optimize WPP bids in the price-maker setting. We formulate the strategic bidding problem as a contextual multi-armed bandit, ensuring provable regret minimization. The algorithm's performance is evaluated against various benchmark strategies using a numerical simulation of the German day-ahead and real-time markets.

Soft robotics holds transformative potential for enabling adaptive and adaptable systems in dynamic environments. However, the interplay between morphological and control complexities and their collective impact on task performance remains poorly understood. Therefore, in this study, we investigate these trade-offs across tasks of differing difficulty levels using four well-used morphological complexity metrics and control complexity measured by FLOPs. We investigate how these factors jointly influence task performance by utilizing the evolutionary robot experiments. Results show that optimal performance depends on the alignment between morphology and control: simpler morphologies and lightweight controllers suffice for easier tasks, while harder tasks demand higher complexities in both dimensions. In addition, a clear trade-off between morphological and control complexities that achieve the same task performance can be observed. Moreover, we also propose a sensitivity analysis to expose the task-specific contributions of individual morphological metrics. Our study establishes a framework for investigating the relationships between morphology, control, and task performance, advancing the development of task-specific robotic designs that balance computational efficiency with adaptability. This study contributes to the practical application of soft robotics in real-world scenarios by providing actionable insights.

In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane selection but fail to leverage problem-specific structural features. Recent machine learning approaches use neural networks for cut selection but focus narrowly on the efficiency of single-node within the B&C algorithm, without considering the broader contextual information. To address this, we propose Global Cut Selection (GCS), which uses a bipartite graph to represent the search tree and combines graph neural networks with reinforcement learning to develop cut selection strategies. Unlike prior methods, GCS applies cutting planes across all nodes, incorporating richer contextual information. Experiments show GCS significantly improves solving efficiency for synthetic and large-scale real-world MIPs compared to traditional and learning-based methods.

A key trait of stochastic optimizers is that multiple runs of the same optimizer in attempting to solve the same problem can produce different results. As a result, their performance is evaluated over several repeats, or runs, on the problem. However, the accuracy of the estimated performance metrics depends on the number of runs and should be studied using statistical tools. We present a statistical analysis of the common metrics, and develop guidelines for experiment design to measure the optimizer's performance using these metrics to a high level of confidence and accuracy. To this end, we first discuss the confidence interval of the metrics and how they are related to the number of runs of an experiment. We then derive a lower bound on the number of repeats in order to guarantee achieving a given accuracy in the metrics. Using this bound, we propose an algorithm to adaptively adjust the number of repeats needed to ensure the accuracy of the evaluated metric. Our simulation results demonstrate the utility of our analysis and how it allows us to conduct reliable benchmarking as well as hyperparameter tuning and prevent us from drawing premature conclusions regarding the performance of stochastic optimizers.