An interior point method for solving semidefinite programs using cutting planes and weighted analytic centers

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed

Applications of operation research in Zakah administration

The significance of the Zakah institution to any Islamic economy, it links to financial viability and economic progress has made it a must to modernize the sector to go in line with modern realities. Poor management of Zakah institutions has been described as detrimental to the efforts of these institutions to collect and disburse Zakah effectively. This paper looks at applications of mathematical and quantitative techniques with the view to achieving optimality and efficiency in business of collection and disbursement of Zakah. The mathematical applications tested are the techniques of contribution maximization, programming, and game theory. The potential applications of this field of mathematics to Zakah operations are vast. It calls for concerted efforts and focuses by researchers, policymakers and Islamic scholars on finding the most efficient way of deploying operation research techniques in the management of Zakah institutions. &nbsp

Monte Carlo algorithms for the detection of necessary linear matrix inequality constraints

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor. A necessary LMI is one whose removal changes the feasible region defined by all the LMI constraints. The general problem of checking whether or not a particular LMI is necessary is NP-complete. However, the methods we describe are polynomial in each iteration, and the number of iterations can be limited by stopping rules. This provides a practical method for reducing the size of some large Semidefinite Programming problems before one attempts to solve them. We demonstrate the applicability of this approach to solving instances of the Lowner ellipsoid problem. We also consider the problem of classification of all the constraints of a semidefinite programming problem as redundant or necessary

On Second-Order Cone Functions

We consider the second-order cone function (SOCF) $f: {\mathbb R}^n \to \mathbb R$ defined by $f(x)= c^T x + d -\|A x + b \|$. Every SOCF is concave. We give necessary and sufficient conditions for strict concavity of $f$. The parameters $A \in {\mathbb R}^{m \times n}$ and $b \in {\mathbb R}^m$ are not uniquely determined. We show that every SOCF can be written in the form $f(x) = c^T x + d -\sqrt{\delta^2 + (x-x_*)^TM(x-x_*)}$. We give necessary and sufficient conditions for the parameters $c$, $d$, $\delta$, $M = A^T A$, and $x_*$ to be uniquely determined. We also give necessary and sufficient conditions for $f$ to be bounded above.Comment: 21 pages, 5 figure

The impact of online banking on the performance of Nigerian banking sector

In this contemporary life, information technology (IT) has become a significant medium in economic and social development.Banking sector nowadays cannot move forward rapidly without the use of IT. In particular, online banking (ebanking) is one of the IT applications with the highest impact on the global economy in creating a new business environment in the sector.Therefore, the aim of this study is to examine the impact of e-banking on the performance of the banking sector in Nigeria.E-banking will be measured by the expenditure made on information and communication technology (ICT) investments, number of debit cards issued to customers, and number of automated teller machines (ATMs) installed by the banks. Return on assets (ROA), return on equity (ROE), and net interest margin (NIM) will be used as performance variables.The impact of ebanking on the bank performance will be examined in two periods: pre-consolidation (i.e., before adopting the e-banking) and post-consolidation (i.e., after adopting the e-banking). Data collection involves secondary data gathered via annual reports of 21 Nigerian banks.The SPSS software will be used for data analysis

A probabilistic method for detecting multivariate extreme outliers

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem

THE EFFECT OF WELL DEPTH ON PHYSICOCHEMICAL VARIATIONIN NEIBOURING VILLAGES OF RIVER NIGER AND BENUE IN LOKOJA KOGI STATE

The effects of well depth on the physicochemical properties of well water of neighboring villages in close proximity to Rivers Niger and Benue were investigated. Wells of to 2.8m depth and 300m distance from the River were selected. These parameters were measured according to the standard method. A total of 120 samples of well waterfrom these villages (Shintaku, Ganaja village, Gbobe and Lokoja metropolis) were taken and analyzed. Results showed that Total Suspended Solid, (TSS), Total Dissolved Solid (TDS),Total Solid (TS),turbidity, alkalinity andTotal Hardness(TH), shows a range of 13-450mgL -1, 57-905mgl-1, 10-170mgL -1,0.611-140NTU 11.5-18mgl-1 and 202-818mgl-1 .Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD) and Dissolved Oxygen (DO), shows a range of0.1-0.45mgl-1, 108-346mgL-1and 0.08-0.75 mgl-1 while Electrical Conductivity (EC) and pH shows a range of 53.5-98.5µscm-1 and 5.9-7.5.  Ammonia, nitrate and phosphate alsoshow a range of 0.01-0.3mgl -1, 3.9-43mgl -1 and 1.5-14.95mgl-1 in the dry seasonrespectively. Total Suspended Solid,(TSS), Total Dissolved Solid (TDS), Total Solid (TS), turbidity, alkalinity and Total Hardness(TH), shows a range of 13-450mgl-1, 57-905mgl-1, 10-170mgl-1, 0.611-140 NTU, 59-131 mgl-1 and 130-404 mgl-1 .  Biochemical Oxygen Demand (BOD), Chemical Oxygen Demand (COD)  and Dissolved Oxygen (DO) shows a range of 0.2-31 mgl-1, 60-818 mgl-1 and 0.9 - 1.2 mgl-1,Electrical Conductivity (EC) and pH shows a range of 0.611-140 NTU and. Ammonia, nitrate and phosphate show a range of3.1-14.5mgl-1, 7.5 -65mgl-1and 3.1-13.5mgl-1 respectively. During the wet season, it was found that the nitrate, turbidity and pH increased with depth of the well and the values of TS and TDS also increases positively with the wells proximity to the river in wet season, which was evident in their R2 Values (correlation coefficient) as they range from 0.7-0.8. Careful consideration and planning is needed in construction of the wells. This suggests that wells must be up to 15m deep and 300m distance away from the river so as to be free from pollution. Key words: Physico-chemical, Well, River Niger, Benue, Parameter

Effect of educational intervention on knowledge about hypertension and factors predicting adherence to drug therapy

The present study was aimed at identifying the degree of knowledge of people with hypertension about the disease, identifying the factors predicting adherence to therapy and administering intervention. It was a quasi-experimental study involving 600 patients selected by multistage sampling technique. Adherence status was assessed using Morisky medication adherence scale8. Knowledge was measured using an eight-item instrument. Educational intervention in form of group discussions was administered. Values of p ≤ 0.05 were considered statistically significant. BP control was significantly higher in those that adhered to antihypertensive medication compared with non-adhering patients (χ2 = 14.526; df = 1; p-value = < 0.001). Comorbidity and number of antihypertensive drugs the patients were taking were found to be the predictors of adherence. After intervention, the percentage of respondents with good adherence increased from 41.3% to 48.3% (p = 0.369) in the intervention group. Furthermore educational intervention had a positive effect on knowledge of the respondents [from 64% to 66.3% (p= 0.623)] in the intervention group. The results revealed that the educational intervention had positive impact of knowledge of hypertension and its treatment. Additionally, Comorbidity and number of antihypertensive prescribed were found to be the predictors of adherence to medications.&nbsp

Stock Market Linkage, Financial Contagion and Assets Price Movements: Evidence from Nigerian Stock Exchange

This paper studied portfolio-investments diversification, stock market linkage and negative integration in Nigerian stock exchange. Like many other stock exchanges around the world, Nigerian stock exchange was devastated by the global financial crisis of 2008. That single crisis has changed the mode of operations of the market by affecting market capitalisation, efficiency and profit. Ten stock market indices are involved in this study, where the aim is to find out how Nigerian stock markets relate with counterparts around the world. The study covered the period from September 2009 to August 2016. The study used Generalised Impulse response function, Engel-Granger cointegration and Johansen cointegration analysis to measure integration between Nigerian stock exchange and selection of nine stock exchanges around the world. The results from cointegration analysis show lack of cointegration. This means despite globalisation Nigerian stock exchange is less integrated with the rest of the stock markets providing ample opportunities for portfolio diversification. This also further support previous studies that found out that developed countries stock markets tend to correlate with their developed countries counterparts than emerging and developing markets

Nigerian economy: business, governance and investment in period of crisis

Nigerian economy is very sensitive to happenings in the global crude oil market due to Nigeria dependence on the black gold. The recession Nigeria found herself in 2016 was mainly caused by the fall in the international price of crude oil. It is the same factor that also help to explain Buhari government massive borrowings to help close the gap in government budget since coming to power in 2015. In the years since independence, Nigerian economy has changed from its largely agrarian state of 1960s to an import depended mono-economy. Nigeria single most important export for more than forty years has remain crude oil. But, in the period since independence various economic models have been tested, as many as there were changes in governments. While the adaptation of some of these economic programs were domestically inspired, others were forced on Nigeria from the outside. The book provides a comprehensive account of Nigerian economy, taking into consideration the changes that have taken place in the last one decade