Minimization Problem Research Articles

Generalized and Robust Least Squares Regression.

As a simple yet effective method, least squares regression (LSR) is extensively applied for data regression and classification. Combined with sparse representation, LSR can be extended to feature selection (FS) as well, in which l1 regularization is often applied in embedded FS algorithms. However, because the loss function is in the form of squared error, LSR and its variants are sensitive to noises, which significantly degrades the effectiveness and performance of classification and FS. To cope with the problem, we propose a generalized and robust LSR (GRLSR) for classification and FS, which is made up of arbitrary concave loss function and the l2,p -norm regularization term. Meanwhile, an iterative algorithm is applied to efficiently deal with the nonconvex minimization problem, in which an additional weight to suppress the effect of noises is added to each data point. The weights can be automatically assigned according to the error of the samples. When the error is large, the value of the corresponding weight is small. It is this mechanism that allows GRLSR to reduce the impact of noises and outliers. According to the different formulations of the concave loss function, four specific methods are proposed to clarify the essence of the framework. Comprehensive experiments on corrupted datasets have proven the advantage of the proposed method.

NOMA Assisted Two-Tier VR Content Transmission: A Tile-Based Approach for QoE Optimization

Virtual reality (VR) provides users with an immersive and interactive experience through head-mounted devices, which has attracted increasing attention in recent years. Specifically, tile-based VR content transmission provides a promising approach to alleviate the conflict between limited bandwidth and high-performance requirements (e.g., high-resolution and low-delay). However, the tiling pattern affects the encoding efficiency and visual distortion of the VR content. Accounting for this issue, in this paper, a quality of experience (QoE)-aware cost minimization problem is investigated for a tile-based VR content transmission scenario. In particular, an edge server (ES) co-located at a cellular base station (BS) separates its generated VR content into several tiles according to the tiling pattern selection, and a weighted-to-spherically-uniform quality model is used to evaluate the effect of different tiling patterns on QoE. Moreover, to improve the transmission performance between the edge server and VR users (VRUs), unmanned aerial vehicles (UAVs) are leveraged as relay points to provide line of sight channels. Then, we formulate an optimization problem to minimize the sum of weighted total energy consumption and VR content distortion (i.e., QoE-aware cost) by jointly optimizing the tiling pattern selections, the VRUs-UAV grouping, partial computing decisions, and resource allocation. The formulated problem is a mixed integer non-linear programming problem, which is challenging to solve. To address this difficulty, we equivalently decompose the formulated problem into three subproblems and propose corresponding algorithms to solve them, respectively. Numerical results demonstrate that our proposed solution can effectively reduce the QoE-aware cost for VR content transmission in comparison with other baseline algorithms.

Isogeometric Shape Optimization of Reissner–Mindlin Shell with Analytical Sensitivity and Application to Cellular Sandwich Structures

Structural shape optimization plays a significant role in structural design, as it can find an appropriate layout and shape to improve structural performance. Isogeometric analysis provides a promising framework for structural shape optimization, unifying the design model and analysis model in the optimization process. This paper presents an adjoint-based analytical sensitivity for isogeometric shape optimization of Reissner–Mindlin shell structures. The shell structures are modeled by multiple NURBS surfaces and design variables are associated with the position of control points. A multilevel approach is performed with a coarse mesh for the design model and a dense mesh for the analysis model. The sensitivity propagation is achieved through a transformation matrix between the design and analysis models. Structural compliance minimization problems with and without constraints are studied and the optimization history shows that the optimization can converge quickly within fewer iterations. The developed formulations are validated through several numerical examples and applied to the optimization of cellular sandwich structures, which are widely used in engineering applications. Numerical results show that optimized sandwich panels can achieve better performance in bending resistance.

Multi-agent reinforcement learning based computation offloading and resource allocation for LEO Satellite edge computing networks

Due to the limitations caused by geographical conditions and economic requirements, it is difficult to provide computing services by terrestrial networks for mobile terminals in remote areas. To address this issue, mobile edge computing (MEC) servers can be deployed in the low earth orbit (LEO) satellites to act as a complement and accommodate the unserved terminals. However, offloading computing tasks to servers in satellites may increase the energy consumption of ground terminals. Considering the limited battery capacity of ground terminals, how to perform the computation offloading and resource allocation are key challenges in the LEO satellite edge computing networks. Therefore, in this paper, we investigate the energy minimization problem for LEO satellite edge computing networks, where a multi-agent deep reinforcement learning algorithm with global rewards is proposed to optimize the transmit power, CPU frequency, bit allocation, offloading decision and bandwidth allocation via a decentralized method. Simulation results show that our proposed algorithm can converge faster. Most importantly, compared with the random algorithm, the proximal policy optimization (PPO) algorithm, and the deep deterministic policy gradient (DDPG) algorithm, the ground terminals’ energy consumption can be effectively reduced by our proposed algorithm.

Predictor‐based collision‐free and connectivity‐preserving resilient formation control for multi‐agent systems under sensor deception attacks

AbstractMalicious attack is a potential threat to collision‐free and connectivity‐preserving formation. In this article, a predictor‐based collision‐free and connectivity‐preserving resilient formation control strategy is proposed for a class of multi‐agent systems under sensor deception attacks. The predictor states are constructed to replace original states in the control strategy, and a novel attack compensator is constructed to suppress sensor deception attacks. Prediction errors, instead of compromised errors, are introduced to update weights of radial basis function neural networks (RBFNNs). To achieve collision avoidance and connectivity preservation, a transformation function in logarithmic form is introduced. To avoid static and dynamic obstacles, an improved artificial potential function (APF) combined with their velocity information is constructed. Furthermore, to solve the local minimum problem in the combining of transformation function and APF, a virtual force is added. Based on the Lyapunov function, all closed‐loop signals are bounded and collision‐free and connectivity‐preserving formation is achieved. The simulation related to a group of quadrotors verifies the effectiveness of the proposed resilient control strategy.

CGE Analysis of the Impact of the 2024 Minimum Wage Increase on the National Economy in Indonesia

One of the minimum wage problems is caused by workers/laborers' needing to agree with the wage increase set. The minimum wage increase is still minimal compared to the high worker need. The Labor Organization president called the government to raise the provincial minimum wage (UMP) and district/city minimum wage (UMK) 2024 by 15%. This figure is obtained from the Decent Living Needs (KHL) survey results and other indicators such as inflation and economic growth. On the other hand, the minimum wage increase of 15% is considered by employers to be unrealistic, considering the condition of the national economy is hit by uncertainty. The government said that determining the minimum wage based on PP 36/2021 and considering the welfare of workers/laborers’ also looks at the Company's capabilities. This paper aims to see new macroeconomic and welfare conditions due to the increase in the minimum wage by 15%. Using the general equilibrium model of static computing (CGE), the analysis results show that an increase in the minimum wage leads to a decrease in demand for labor, especially in labor-intensive sectors. The increase in wages impacts increasing household income, thus indicating an increase in household welfare. However, inflationary pressures brought about by the minimum wage increase mask the increase in revenue, resulting in a decrease in household consumption budgets. This translates into a loss of net well-being, with a more significant impact on urban households than rural households. The output of most sectors, especially labor-intensive sectors, declined, but nominal GDP increased. The increase in nominal GDP is due to rising prices, not actual economic output.

Mathematical Models for the Single-Channel and Multi-Channel PMU Allocation Problem and Their Solution Algorithms

Phasor measurement units (PMUs) are deployed at power grid nodes around the transmission grid, determining precise power system monitoring conditions. In real life, it is not realistic to place a PMU at every power grid node; thus, the lowest PMU number is optimally selected for the full observation of the entire network. In this study, the PMU placement model is reconsidered, taking into account single- and multi-capacity placement models rather than the well-studied PMU placement model with an unrestricted number of channels. A restricted number of channels per monitoring device is used, instead of supposing that a PMU is able to observe all incident buses through the transmission connectivity lines. The optimization models are declared closely to the power dominating set and minimum edge cover problem in graph theory. These discrete optimization problems are directly related with the minimum set covering problem. Initially, the allocation model is declared as a constrained mixed-integer linear program implemented by mathematical and stochastic algorithms. Then, the 0/1 integer linear problem is reformulated into a non-convex constraint program to find optimality. The mathematical models are solved either in binary form or in the continuous domain using specialized optimization libraries, and are all implemented in YALMIP software in conjunction with MATLAB. Mixed-integer linear solvers, nonlinear programming solvers, and heuristic algorithms are utilized in the aforementioned software packages to locate the global solution for each instance solved in this application, which considers the transformation of the existing power grids to smart grids.

On the convergence of gradient descent for robust functional linear regression

Functional data analysis offers a set of statistical methods concerned with extracting insights from intrinsically infinite-dimensional data and has attracted considerable amount of attentions in the past few decades. In this paper, we study robust functional linear regression model with a scalar response and a functional predictor in the framework of reproducing kernel Hilbert spaces. A gradient descent algorithm with early stopping is introduced to solve the corresponding empirical risk minimization problem associated with robust loss functions. By appropriately selecting the early stopping rule and the scaling parameter of the robust losses, the convergence of the proposed algorithm is established when the response variable is bounded or satisfies a moment condition. Explicit learning rates with respect to both estimation and prediction error are provided in terms of regularity of the regression function and eigenvalue decay rate of the integral operator induced by the reproducing kernel and covariance function.

MUSCAT: Distributed multi-agent Q-learning-based minimum span channel allocation technique for UAV-enabled wireless networks

We consider a minimum span channel allocation problem (MS-CAP) to overcome spectrum scarcity and facilitate the efficiency of unmanned aerial vehicle (UAV)-enabled wireless networks. Basically, the MS-CAP minimizes the difference between the maximum and minimum used frequency, i.e., the required total bandwidth, while guaranteeing the quality-of-service (QoS) requirements for each wireless link in the network. The conventional optimal minimum span channel allocation (MS-CA) scheme is based on a centralized approach, assuming that global network information is available at the central controller. In practice, however, this may not be feasible for dynamic environments like UAV-enabled wireless networks since the real-time exchange of network information and channel allocation results with dynamically moving UAVs is formidable. Hence, we propose a novel practical MS-CA algorithm based on distributed multi-agent reinforcement learning (MARL), where each agent independently learns its best strategy with its local observations. To the best of our knowledge, the proposed technique is the first work of designing a distributed MARL for the MS-CAP for multi-UAV-enabled wireless networks in the literature. Numerical results reveal that the proposed distributed MS-CA technique can efficiently save the required total bandwidth while ensuring the QoS requirements of each link, represented by the signal-to-interference plus noise ratio (SINR) threshold, even in dynamic wireless networks. It validates the applicability of the proposed distributed MS-CA framework to dynamic networks.

Minimizing Task Age upon Decision for Low-Latency MEC Networks Task Offloading with Action-Masked Deep Reinforcement Learning.

In this paper, we consider a low-latency Mobile Edge Computing (MEC) network where multiple User Equipment (UE) wirelessly reports to a decision-making edge server. At the same time, the transmissions are operated with Finite Blocklength (FBL) codes to achieve low-latency transmission. We introduce the task of Age upon Decision (AuD) aimed at the timeliness of tasks used for decision-making, which highlights the timeliness of the information at decision-making moments. For the case in which dynamic task generation and random fading channels are considered, we provide a task AuD minimization design by jointly selecting UE and allocating blocklength. In particular, to solve the task AuD minimization problem, we transform the optimization problem to a Markov Decision Process problem and propose an Error Probability-Controlled Action-Masked Proximal Policy Optimization (EMPPO) algorithm. Via simulation, we show that the proposed design achieves a lower AuD than baseline methods across various network conditions, especially in scenarios with significant channel Signal-to-Noise Ratio (SNR) differences and low average SNR, which shows the robustness of EMPPO and its potential for real-time applications.

A new algorithm for computing the nearest polynomial to multiple given polynomials via weighted ℓ2,q-norm minimization and its complex extension

A new algorithm is proposed in this paper for computing the nearest polynomial to multiple given polynomials with a given zero in the real case, where the distance between polynomials is defined by the weighted ℓ2,q norm (0<q≤2). First, the problem is formulated as a univariate constrained non-convex minimization problem, where prior information of the coefficients of the polynomial can be embedded by selecting proper weights. Then, an iteratively reweighted algorithm is designed to solve the obtained problem, and also the convergence and rate of convergence are uniformly demonstrated for all q in (0,2]. Since all the existing methods for computing the nearest polynomial to multiple given polynomials with a given zero are limited to the real case, we ingeniously extend the results to the complex case. Finally, two representative examples that separately compute the nearest real and complex polynomials are presented to show the effectiveness of the proposed algorithm.

Robust elastic full-waveform inversion using an alternating direction method of multipliers with reconstructed wavefields

Elastic full-waveform inversion (EFWI) is a process used to estimate subsurface properties by fitting seismic data while satisfying wave propagation physics. The problem is formulated as a least-squares data fitting minimization problem with two sets of constraints: partial-differential equation (PDE) constraints governing elastic wave propagation and physical model constraints implementing prior information. The alternating direction method of multipliers is used to solve the problem, resulting in an iterative algorithm with well-conditioned subproblems. Although wavefield reconstruction is the most challenging part of the iteration, sparse linear algebra techniques can be used for moderate-sized problems and frequency domain formulations. The Hessian matrix is blocky with diagonal blocks, making model updates fast. Gradient ascent is used to update Lagrange multipliers by summing PDE violations. Various numerical examples are used to investigate algorithmic components, including model parameterizations, physical model constraints, the role of the Hessian matrix in suppressing interparameter cross-talk, computational efficiency with the source sketching method, and the effect of noise and near-surface effects.

Potential Energy Optimization Approach in the Form-Finding of Tensegrities and Cable–Strut Systems

A form-finding process for tensegrities and cable–strut systems is determined as a minimum problem of potential energy that is constructed considering initial estimated pre-stress states. Both the Jacobian and Hessian matrices of a potential energy function are derived explicitly regarding free nodal coordinates. Based on these derivations, both the first-order geodesic dynamic relaxation optimization method and the second-order optimization method of Newton can be applied to solve form-finding problems involving tensegrities and cable–strut structures. It should be noted that both the pre-stress state and the configuration of the systems are adjusted during the optimization process to satisfy self-equilibrium conditions. The geometrical constraints are then included in the proposed work as equality constraint conditions to find the final forms satisfying not only the self-equilibrium states but also the designers’ demands. Two well-known and complex systems are investigated to assess the efficiency of the proposed method, i.e. free-standing truncated icosahedral tensegrity and the Kiewitt Dome.

A novel variational approach for multiphoton microscopy image restoration: from PSF estimation to 3D deconvolution

In multi-photon microscopy (MPM), a recent in-vivo fluorescence microscopy system, the task of image restoration can be decomposed into two interlinked inverse problems: firstly, the characterization of the point spread function (PSF) and subsequently, the deconvolution (i.e. deblurring) to remove the PSF effect, and reduce noise. The acquired MPM image quality is critically affected by PSF blurring and intense noise. The PSF in MPM is highly spread in 3D and is not well characterized, presenting high variability with respect to the observed objects. This makes the restoration of MPM images challenging. Common PSF estimation methods in fluorescence microscopy, including MPM, involve capturing images of sub-resolution beads, followed by quantifying the resulting ellipsoidal 3D spot. In this work, we revisit this approach, coping with its inherent limitations in terms of accuracy and practicality. We estimate the PSF from the observation of relatively large beads (approximately 1 μm in diameter). This goes through the formulation and resolution of an original non-convex minimization problem, for which we propose a proximal alternating method along with convergence guarantees. Following the PSF estimation step, we then introduce an innovative strategy to deal with the high level multiplicative noise degrading the acquisitions. We rely on a heteroscedastic noise model for which we estimate the parameters. We then solve a constrained optimization problem to restore the image, accounting for the estimated PSF and noise, while allowing a minimal hyper-parameter tuning. Theoretical guarantees are given for the restoration algorithm. These algorithmic contributions lead to an end-to-end pipeline for 3D image restoration in MPM, that we share as a publicly available Python software. We demonstrate its effectiveness through several experiments on both simulated and real data.

Benders decomposition algorithms for minimizing the spread of harmful contagions in networks

The COVID-19 pandemic has been a recent example for the spread of a harmful contagion in large populations. Moreover, the spread of harmful contagions is not only restricted to an infectious disease, but is also relevant to computer viruses and malware in computer networks. Furthermore, the spread of fake news and propaganda in online social networks is also of major concern. In this study, we introduce the measure-based spread minimization problem (MBSMP), which can help policy makers in minimizing the spread of harmful contagions in large networks. We develop exact solution methods based on branch-and-Benders-cut algorithms that make use of the application of Benders decomposition method to two different mixed-integer programming formulations of the MBSMP: an arc-based formulation and a path-based formulation. We show that for both formulations the Benders optimality cuts can be generated using a combinatorial procedure rather than solving the dual subproblems using linear programming. Additional improvements such as using scenario-dependent extended seed sets, initial cuts, and a starting heuristic are also incorporated into our branch-and-Benders-cut algorithms. We investigate the contribution of various components of the solution algorithms to the performance on the basis of computational results obtained on a set of instances derived from existing ones in the literature.

Scene recovery: Combining visual enhancement and resolution improvement

Visibility enhancement of outdoor images under complex imaging conditions has been a crucial task for computer vision and received growing attention. However, existing image enhancement methods could result in typical block-like artifacts or color distortion. The undesirable impurities might also be significantly magnified after the enhancement task, further reducing the image quality. For enhancing and super-resolving complex real-world degradation, we propose a simultaneous visual enhancement and resolution improvement (VERI) variational scene recovery model for jointly enhancing image visibility and improving the resolution of the degraded image. Particularly, we estimate the scattering light map for degradation images to achieve clean scene radiance and simultaneously seek a high-quality image through a deep super-resolution network. The semi-proximal alternating direction method of multipliers (sPADMM) algorithm is employed for efficiently solving the minimization problems in the proposed model. Extensive experiments illustrate the effectiveness and robustness of the proposed method in dealing with various scenes, such as haze, sandstorm, underwater or low illumination.

Convergence of inertial prox-penalization and inertial forward–backward algorithms for solving monotone bilevel equilibrium problems

The main focus of this paper is on bilevel optimization on Hilbert spaces involving two monotone equilibrium bifunctions. We present a new achievement consisting on the introduction of inertial methods for solving these types of problems. Indeed, two several inertial type methods are suggested: a proximal algorithm and a forward–backward one. Under suitable conditions and without any restrictive assumption on the trajectories, the weak and strong convergence of the sequence generated by the both iterative methods are established. Two particular cases illustrating the proposed methods are thereafter discussed with respect to hierarchical minimization problems and equilibrium problems under a saddle point constraint. Furthermore, numerical examples are given to demonstrate the implementability of our algorithms. The algorithms and their convergence results improve and develop previous results in the field.

An optimal control problem for diffusion–precipitation model

We present an optimal control problem associated to a chemical transportation phenomena in a periodic porous medium. Posing controls on the porous part of the medium (distributed control), we set up a convex minimization problem. The main objective of this article is to characterize an arbitrary control to be an optimal control. We establish a relation between the optimal control and the corresponding adjoint state. At first, we analyse the microscopic description of the controlled system, then we homogenised the system by rigorous two-scale convergence method and periodic unfolding method.

Graph Laplace Regularization-based pressure sensor placement strategy for leak localization in the water distribution networks under joint hydraulic and topological feature spaces

Urban water distribution networks (WDNs) have wide range and intricate topology, which include leakage, pipe burst and other abnormal states during production and operation. With the continuous development of the Internet of Things (IoT) technology in recent years, the means of monitoring the WDNs by using wireless sensor network technology has gradually received attention and extensive research. Most of the existing researches select the deployment location of sensors according to the hydraulic state of the WDNs, but the connectivity and topology between the nodes of the WDNs are not fully considered and analyzed. In this study, a new method that can integrate the topological features and hydraulic model information of the WDN is proposed to solve the problem of optimal sensor placement. First, the method preprocesses the covariance matrix of the pressure sensitivity matrix of the water distribution network by a diffusion kernel-based data prefiltering method and obtains the new network topology weights and its Laplacian matrix under the constraints of the network topology through a data-based graphical Laplacian learning method. Then, the sensor placement problem is transformed into a matrix minimum eigenvalue constraint problem by the Graph Laplace Regularization (GLR)-based method, and finally the selection of sensor nodes is accomplished by the method based on Gershgorin Disc Alignment (GDA). The proposed strategy is tested on a passive Hanoi network, an active Net 3 network, and a larger network, PA2, and is compared with some existing methods. The results show that the proposed solution achieves good performance in three different leak localization methods.

Accurate computing paradigm for decoupled harmonic load flow analysis with CONOPT solvers for non-sinusoidal radial distribution systems

In this article, a novel method for performing Decoupled Harmonic Load Flow (DHLF) analysis in radial distribution systems is presented. The proposed method involves solving load flow equations for both fundamental and higher frequencies as constrained minimization problems utilizing a nonlinear programming (NLP) CONOPT solver integrated into the General Algebraic Modeling Systems (GAMS) environment. The effectiveness of the proposed method is assessed across three IEEE test systems: 18-bus, 33-bus, and 69-bus. Five cases of DHLF analysis are taken into consideration. DHLF was performed on standard test systems with incorporated non-linear loads in the first case. Cases two through five examine the DHLF in the presence of distributed generators (DGs), shunt capacitors (SCs), simultaneous DGs and SCs, and electric vehicles (EVs). Comparing the obtained results to those of DHLF analysis tools ETAP and DigSilent, as well as to those found in the literature, proved that the proposed CONOPT solver provides precise solutions.