A class of Increasing Positively Homogeneous functions for which global optimization problem is NP-hard

It is well known that global optimization problems are, generally speaking, computationally infeasible, that is solving them would require an unreasonably large amount of time and/or space. In certain cases, for example, when objective functions and constraints are convex, it is possible to construct a feasible algorithm for solving global optimization problem successfully. Convexity, however, is not a phenomenon to be often expected in the applications. Nonconvex problems frequently arise in many industrial and scienti¯c areas. Therefore, it is only natural to try to replace convexity with some other structure at least for some classes of nonconvex optimization problems to render the global optimization problem feasible. A theory of abstract convexity has been developed as a result of the above considerations. Monotonic analysis, a branch of abstract convex analysis, is analogous in many ways to convex analysis, and sometimes is even simpler. It turned out that many problems of nonconvex optimization encountered in applications can be described in terms of monotonic functions. The analogies with convex analysis were considered to aid in solving some classes of nonconvex optimization problems. In this thesis we will focus on one of the elements of monotonic analysis - Increasing Positively Homogeneous functions of degree one or in short IPH functions. The aim of present research is to show that finding the solution and ²-approximation to the solution of the global optimization problem for IPH functions restricted to a unit simplex is an NP-hard problem. These results can be further extended to positively homogeneous functions of degree ´, ´ > 0.Master of Mathematical Sciences (Research

How are we progressing with academic numeracy at regional universities? Perspectives from first-year undergraduate studies

This study provides an overview of the support provided for academic numeracy for first-year students across six Australian regional universities. Survey analysis of university academics provided an overview of the approaches used in academic numeracy in diverse cohorts. Further investigations via semi-structured interviews and secondary data were performed, providing details of the level of academic numeracy required in the subjects offered, identification of at-risk students and strategies for student support, and student responses to service provision. A case study at one university provided a more detailed view of the factors influencing attrition in first-year academic numeracy subjects. This case study highlighted issues related to a one-size-fits-all approach and findings argue for a more nuanced cohort-based approach that combines conventional statistical analysis with analysis that provides a more detailed view of complex scenarios. The study suggests that while support services are not responding well to the issue of attrition, better targeting individual student support may lead to improvements. © 2020, Mathematics Education Research Group of Australasia, Inc. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Nargiz Sultanova ” is provided in this record** Sultanova, Nargi

Matching algorithms : fundamentals, applications and challenges

Matching plays a vital role in the rational allocation of resources in many areas, ranging from market operation to people's daily lives. In economics, the term matching theory is coined for pairing two agents in a specific market to reach a stable or optimal state. In computer science, all branches of matching problems have emerged, such as the question-answer matching in information retrieval, user-item matching in a recommender system, and entity-relation matching in the knowledge graph. A preference list is the core element during a matching process, which can either be obtained directly from the agents or generated indirectly by prediction. Based on the preference list access, matching problems are divided into two categories, i.e., explicit matching and implicit matching. In this paper, we first introduce the matching theory's basic models and algorithms in explicit matching. The existing methods for coping with various matching problems in implicit matching are reviewed, such as retrieval matching, user-item matching, entity-relation matching, and image matching. Furthermore, we look into representative applications in these areas, including marriage and labor markets in explicit matching and several similarity-based matching problems in implicit matching. Finally, this survey paper concludes with a discussion of open issues and promising future directions in the field of matching. © 2017 IEEE. **Please note that there are multiple authors for this article therefore only the name of the first 5 including Federation University Australia affiliate “Jing Ren, Xia Feng, Nargiz Sultanova" is provided in this record*

How are we progressing with academic numeracy at regional universities? Perspectives from first-year undergraduate studies

This study provides an overview of the support provided for academic numeracy for first-year students across six Australian regional universities. Survey analysis of university academics provided an overview of the approaches used in academic numeracy in diverse cohorts. Further investigations via semi-structured interviews and secondary data were performed, providing details of the level of academic numeracy required in the subjects offered, identification of at-risk students and strategies for student support, and student responses to service provision. A case study at one university provided a more detailed view of the factors influencing attrition in first-year academic numeracy subjects. This case study highlighted issues related to a one-size-fits-all approach and findings argue for a more nuanced cohort-based approach that combines conventional statistical analysis with analysis that provides a more detailed view of complex scenarios. The study suggests that while support services are not responding well to the issue of attrition, better targeting individual student support may lead to improvements

Aggregate subgradient smoothing mehtods for large scale nonsmooth nonconvex optimisation and applications

Nonsmooth optimisation problems are problems which deal with minimisation or maximisation of functions that are not necessarily differentiable. They arise frequently in many practical applications, for example in engineering, machine learning and economics. In addition, some smooth problems can be reformulated as nonsmooth optimisation problems with a simpler structure or a smaller dimension. Despite the fact that there exist many algorithms for solving nonsmooth optimisation problems, the field is still very much in development. Nonsmooth nonconvex optimisation, in particular, is far from being considered a mature branch of optimisation

Reconstruction of tropical cyclone and depression proxies for the South Pacific since the 1850s

Southwest Pacific nations are highly vulnerable to extreme weather and climate events, particularly those associated with synoptic-scale systems such as tropical cyclones (TCs) and depressions (TDs). This study utilises the Okubo–Weiss–Zeta parameter (OWZP) method to reconstruct historical records of both TCs and TDs for the South Pacific basin using state-of-the-art NOAA-CIRES Twentieth Century Reanalysis (20CR) product. Extensive statistical assessments of these reconstructions are carried out using observational records for the satellite period (i.e., 1979–2014) as ‘ground-truths’. Results show that 20CR-derived TCs and TDs resemble several key characteristics of the observational records, including spatial distribution of genesis locations and track shapes. This gives us confidence that the 20CR-derived long-term records of TCs and TDs can serve as an effective tool for examining historical changes in various characteristics of TCs and TDs, particularly in the context of anthropogenic climate change. © 202

Tropical cyclones and depressions over the South Pacific Ocean since the late 19th century : assessing synergistic relationship between the El Niño Southern Oscillation and Interdecadal Pacific Oscillation

Tropical cyclones (TCs) and tropical depressions (TDs), hereafter collectively referred to as tropical storms, often exhibit large year-to-year variability in the South Pacific Ocean basin. Many past studies have examined this variability in relation to the El Niño Southern Oscillation (ENSO) phenomenon, particularly using observational data from the post-satellite era (i.e., after the 1970s when TC observations became more consistent). However, less emphasis is placed on how tropical storms are modulated at interdecadal and decadal time scales such as due to Interdecadal Pacific Oscillation (IPO). This is because post-satellite data are available for relatively short time period (i.e., post-1970s), limiting our understanding of the IPO–TC relationship in the South Pacific. Here, using NOAA-CIRES 20th Century Reanalysis (20CR) dataset, we reconstruct historical records (1871–2014) of TC and depression proxies for the South Pacific Ocean basin, and then utilize these reconstructed proxies to first understand the connections between TC–ENSO and TC–IPO over the 20th century, and then investigate the combined effects of ENSO–IPO effects on TCs and depressions. Results show that La Niña (El Niño) is more dominant on TC activity than El Niño (La Niña) over the western subregion 140–170° E (eastern sub-region, 170–220° E) as expected. We also show that TC numbers are strongly modulated by the IPO phenomenon with, on average, more TCs occurring during the positive phase than during the negative phase of the IPO in both western and eastern sub-regions. We show for the first time (using a long-term reconstructed TC dataset) that the combined phases of El Niño and + IPO account for increased TC activity, as opposed to the combined phase of La Niña an

Finding compact and well-separated clusters : clustering using silhouette coefficients

Finding compact and well-separated clusters in data sets is a challenging task. Most clustering algorithms try to minimize certain clustering objective functions. These functions usually reflect the intra-cluster similarity and inter-cluster dissimilarity. However, the use of such functions alone may not lead to the finding of well-separated and, in some cases, compact clusters. Therefore additional measures, called cluster validity indices, are used to estimate the true number of well-separated and compact clusters. Some of these indices are well-suited to be included into the optimization model of the clustering problem. Silhouette coefficients are among such indices. In this paper, a new optimization model of the clustering problem is developed where the clustering function is used as an objective and silhouette coefficients are used to formulate constraints. Then an algorithm, called CLUSCO (CLustering Using Silhouette COefficients), is designed to construct clusters incrementally. Three schemes are discussed to reduce the computational complexity of the algorithm. Its performance is evaluated using fourteen real-world data sets and compared with that of three state-of-the-art clustering algorithms. Results show that the CLUSCO is able to compute compact clusters which are significantly better separable in comparison with those obtained by other algorithms. © 2022 Elsevier Lt