LMBOPT: a limited memory method for bound-constrained optimization

Recently, Neumaier and Azmi gave a comprehensive convergence theory for a generic algorithm for bound constrained optimization problems with a continuously differentiable objective function. The algorithm combines an active set strategy with a gradient-free line search along a piecewise linear search path defined by directions chosen to reduce zigzagging. This paper describes , an efficient implementation of this scheme. It employs new limited memory techniques for computing the search directions, improves by adding various safeguards relevant when finite precision arithmetic is used, and adds many practical enhancements in other details. The paper compares and several other solvers on the unconstrained and bound constrained problems from the collection and makes recommendations on which solver to use and when. Depending on the problem class, the problem dimension, and the precise goal, the best solvers are , , and .

Superconvergent interpolants for Gaussian collocation solutions of mixed order BVODE systems

<abstract><p>The high quality COLSYS/COLNEW collocation software package is widely used for the numerical solution of boundary value ODEs (BVODEs), often through interfaces to computing environments such as Scilab, R, and Python. The continuous collocation solution returned by the code is much more accurate at a set of mesh points that partition the problem domain than it is elsewhere; the mesh point values are said to be superconvergent. In order to improve the accuracy of the continuous solution approximation at non-mesh points, when the BVODE is expressed in first order system form, an approach based on continuous Runge-Kutta (CRK) methods has been used to obtain a superconvergent interpolant (SCI) across the problem domain. Based on this approach, recent work has seen the development of a new, more efficient version of COLSYS/COLNEW that returns an error controlled SCI.</p> <p>However, most systems of BVODEs include higher derivatives and a feature of COLSYS/COLNEW is that it can directly treat such mixed order BVODE systems, resulting in improved efficiency, continuity of the approximate solution, and user convenience. In this paper we generalize the approach mentioned above for first order systems to obtain SCIs for collocation solutions of mixed order BVODE systems. The main contribution of this paper is the derivation of generalizations of continuous Runge-Kutta-Nyström methods that form the basis for SCIs for this more general problem class. We provide numerical results that (ⅰ) show that the SCIs are much more accurate than the collocation solutions at non-mesh points, (ⅱ) verify the order of accuracy of these SCIs, and (ⅲ) show that the cost of utilizing the SCIs is a small fraction of the cost of computing the collocation solution upon which they are based.</p></abstract>

Elastic Energy Management Algorithm Using IoT Technology for Devices with Smart Appliance Functionality for Applications in Smart-Grid

Currently, ensuring the correct functioning of the electrical grid is an important issue in terms of maintaining the normative voltage parameters and local line overloads. The unpredictability of Renewable Energy Sources (RES), the occurrence of the phenomenon of peak demand, as well as exceeding the voltage level above the nominal values in a smart grid makes it justifiable to conduct further research in this field. The article presents the results of simulation tests and experimental laboratory tests of an electricity management system in order to reduce excessively high grid load or reduce excessively high grid voltage values resulting from increased production of prosumer RES. The research is based on the Elastic Energy Management (EEM) algorithm for smart appliances (SA) using IoT (Internet of Things) technology. The data for the algorithm was obtained from a message broker that implements the Message Queue Telemetry Transport (MQTT) protocol. The complexity of selecting power settings for SA in the EEM algorithm required the use of a solution that is applied to the NP difficult problem class. For this purpose, the Greedy Randomized Adaptive Search Procedure (GRASP) was used in the EEM algorithm. The presented results of the simulation and experiment confirmed the possibility of regulating the network voltage by the Elastic Energy Management algorithm in the event of voltage fluctuations related to excessive load or local generation.

Stability Analysis of Multistage One-Step Multiderivative Methods for Nonlinear Impulsive Differential Equations in Banach Spaces

In this paper, we first introduce the problem class K p μ , λ , ζ with respect to the initial value problems of nonlinear impulsive differential equations in Banach spaces. The stability and asymptotic stability results of the analytic solution of the problem class K p μ , λ , ζ are obtained. Then, the numerical stability and asymptotic stability conditions of multistage one-step multiderivative methods are also given. Two numerical experiments are given to confirm the theoretical results in the end.

Improved interval methods for solving circle packing problems in the unit square

In this work computer-assisted optimality proofs are given for the problems of finding the densest packings of 31, 32, and 33 non-overlapping equal circles in a square. In a study of 2005, a fully interval arithmetic based global optimization method was introduced for the problem class, solving the cases 28, 29, 30. Until now, these were the largest problem instances solved on a computer. Using the techniques of that paper, the estimated solution time for the next three cases would have been 3–6 CPU months. In the present paper this former method is improved in both its local and global search phases. We discuss a new interval-based polygon representation of the core local method for eliminating suboptimal regions, which has a simpler implementation, easier proof of correctness, and faster behaviour than the former one. Furthermore, a modified strategy is presented for the global phase of the search, including improved symmetry filtering and tile pattern matching. With the new method the cases $$n=31,32,33$$ n = 31 , 32 , 33 have been solved in 26, 61, and 13 CPU hours, giving high precision enclosures for all global optimizers and the optimum value. After eliminating the hardware and compiler improvements since the former study, the new proof technique became roughly about 40–100 times faster than the previous one. In addition, the new implementation is suitable for solving the next few circle packing instances with similar computational effort.

Rao algorithm-based method for optimisation of steel frames using nonlinear inelastic analysis

Metaheuristic optimisation algorithms have been increasingly used because of their superior ability to find globally optimal solutions. Theoretically, these algorithms are very powerful and can be applied in all types of optimisation problems. However, in reality, their performance depends on the characteristics of each optimisation problem class. In addition, the complexity of an algorithm is an important factor affecting its application in specific design problems. In this paper, the Rao optimisation algorithm, one of the newest metaheuristic algorithms, is presented for the optimisation algorithm of steel frame structures. The advantage of the Rao algorithm is that it is quite simple with few parameters, so engineers can easily apply it in daily design tasks. A nonlinear inelastic analysis is used to consider the nonlinear behaviors of the steel structure. A two-story space steel frame is studied. The results show that Rao-1 is more stable and converged more quickly but easily trapped in local solutions than Rao-2 and Rao-4. Rao-4 is more efficient in global search but its stability is less than other algorithms. Keywords:nonlinear inelastic analysis, optimisation, Rao algorithm, steel frame.

Superfast Second-Order Methods for Unconstrained Convex Optimization

In this paper, we present new second-order methods with convergence rate $$O\left( k^{-4}\right) $$ O k - 4 , where k is the iteration counter. This is faster than the existing lower bound for this type of schemes (Agarwal and Hazan in Proceedings of the 31st conference on learning theory, PMLR, pp. 774–792, 2018; Arjevani and Shiff in Math Program 178(1–2):327–360, 2019), which is $$O\left( k^{-7/2} \right) $$ O k - 7 / 2 . Our progress can be explained by a finer specification of the problem class. The main idea of this approach consists in implementation of the third-order scheme from Nesterov (Math Program 186:157–183, 2021) using the second-order oracle. At each iteration of our method, we solve a nontrivial auxiliary problem by a linearly convergent scheme based on the relative non-degeneracy condition (Bauschke et al. in Math Oper Res 42:330–348, 2016; Lu et al. in SIOPT 28(1):333–354, 2018). During this process, the Hessian of the objective function is computed once, and the gradient is computed $$O\left( \ln {1 \over \epsilon }\right) $$ O ln 1 ϵ times, where $$\epsilon $$ ϵ is the desired accuracy of the solution for our problem.

A Year of Online Classes Amid COVID-19 Pandemic: Advantages, Problems, and Suggestions of Economics Students at a Bangladeshi Public University

Though there have been works highlighting the advantages and disadvantages of online learning, no study focused on university-level economics students. None of the studies explored students' opinions about improving the quality and effectiveness of online classes. Many used questionable samples, closed-ended questions, and all those researches were carried out at the beginning of online classes. In this paper, we overcome these limitations of earlier studies. Using a convenience sampling technique and open-ended questions, we collect data from 154 university-level economics students after being exposed to the online class for a year. Some advantages of online classes are: students can do classes from home without being exposed to health risks, easily accessible, flexible class schedule, students remained connected with the study, it saves costs, reduce the likelihood of semester loss, easy to understand, less stressful, and learning new technologies. Major problems from students' perspectives include network problems, difficulties in understanding the topic, unsuitable for mathematical courses, concentration problem, class not interactive, financial constraint, adverse health impacts, device issues, power outages, unfamiliarity with digital technology, internet problem, and unfixed class-schedule. Disadvantages outnumbered advantages. Students made several suggestions to improve the quality and effectiveness of online classes. Some of the vital suggestions are: using state-of-the-art digital tools, recording and uploading lectures, resolving internet issues, holding classes regularly, higher efforts to make the topics easier, resolving network issues, lowering class duration, institutional support, implementing a fixed class schedule, and introducing online evaluation system.

Remaining Useful Life Estimation of Bearings

In the domain of predictive maintenance, when trying to repli- cate and compare research in remaining useful life estimation (RUL), several inconsistencies and errors were identified in the experimental methodology used by various researchers. This makes the replication and the comparison of results diffi- cult, thus severely hindering both progress in this research do- main and its practical application to industry. We survey the literature to evaluate the experimental procedures that were used, and identify the most common errors and omission in both experimental procedures and reporting. A total of 70 papers on RUL were audited. From this meta- analysis we estimate that approximately 11% of the papers present work that will allow for replication and comparison. Surprisingly, only about 24.3% (17 of the 70 articles) com- pared their results with previous work. Of the remaining work, 41.4% generated and compared several models of their own and, somewhat unsettling, 31.4% of the researchers made no comparison whatsoever. The remaining 2.9% did not use the same data set for comparisons. The results of this study were also aggregated into 3 categories: problem class selec- tion, model fitting best practices and evaluation best practices. We conclude that model evaluation is the most problematic one. The main contribution of the article is a proposal of an ex- perimental protocol and several recommendations that specif- ically target model evaluation. Adherence to this protocol should substantially facilitate the research and application of RUL prediction models. The goals are to promote the collab- oration between scholars and practitioners alike and advance the research in this domain.

Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis Using a Phase Methodology

In “Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis using a Phase Methodology,” Khaleghei and Kim study a maintenance control problem a as partially observable semi-Markov decision process (POSMDP), a problem class that is typically computationally intractable and not amenable to structural analysis. The authors develop a new approach based on a phase methodology where the idea is to view the intractable POSMDP as the limiting problem of a sequence of tractable POMDPs. They show that the optimal control policy can be represented as a control limit policy which monitors the estimated conditional reliability at each decision epoch, and, by exploiting this structure, an efficient computational approach to solve for the optimal control limit and corresponding optimal value is developed.