An interior point algorithm for the general nonlinear programming problem with trust region globalization

This paper attempts to develop an SQP-based interior point technique for solving the general nonlinear programming problem using trust region globalization and the Coleman-Li scaling. The SQP subproblem is decomposed into a normal and a reduced tangential subproblem in the tradition of numerous works on equality constrained optimization, and strict feasibility is maintained with respect to the bounds. This is intended to be an extension of previous work by Coleman & Li and Vicente. Even though no theoretical proofs of convergence are provided, some computational results are presented which indicate that this algorithm holds promise. The computational experiments have been geared towards improving the semi-local convergence of the algorithm; in particular high sensitivity of the speed of convergence with respect to the fraction of the trust region radius allowed for the normal step and with respect to the initial trust region radius are observed. The chief advantages of this algorithm over primal-dual interior point algorithms are better handling of the `sticking problem' and a reduction in the number of variables by elimination of the multipliers of bound constraints

Nonlinear multicriteria optimization and robust optimality

This dissertation attempts to address two important problems in systems engineering, namely, multicriteria optimization and robustness optimization. In fields ranging from engineering to the social sciences designers are very often required to make decisions that attempt to optimize several criteria or objectives at once. Mathematically this amounts to finding the Pareto optimal set of points for these constrained multiple criteria optimization problems which happen to be nonlinear in many realistic situations, particularly in engineering design. Traditional techniques for nonlinear multicriteria optimization suffer from various drawbacks. The popular method of minimizing weighted sums of the multiple objectives suffers from the deficiency that choosing an even spread of 'weights' does not yield an even spread of points on the Pareto surface and further this spread is often quite sensitive to the relative scales of the functions. A continuation/homotopy based strategy for tracing out the Pareto curve tries to make up for this deficiency, but unfortunately requires exact second derivative information and further cannot be applied to problems with more than two objectives in general. Another technique, goal programming, requires prior knowledge of feasible goals which may not be easily available for more than two objectives. Normal-Boundary Intersection (NBI), a new technique introduced in this dissertation, overcomes all of the difficulties inherent in the existing techniques by introducing a better parametrization of the Pareto set. It is rigorously proved that NBI is completely independent of the relative scales of the functions and is quite successful in producing an evenly distributed set of points on the Pareto set given an evenly distributed set of 'NBI parameters' (comparable to the 'weights' in minimizing weighted sums of objectives). Further, this method can easily handle more than two objectives while retaining the computational efficiency of continuation-type algorithms, which is an improvement over homotopy techniques for tracing the trade-off curve. Various aspects of NBI including computational issues and its relationships with minimizing convex combinations and goal programming are discussed in this dissertation. Finally some case studies from engineering disciplines are performed using NBI. The other facet of this dissertation deals with robustness optimization, a concept useful in quantifying the stability of an optimum in the face of random fluctuations in the design variables. This robustness optimization problem is presented as an application of multicriteria optimization since it essentially involves the simultaneous minimization of two criteria, the objective function value at a point and the dispersion in the function values in a neighborhood of the point. Moreover, a formulation of the robustness optimization problem is presented so that it fits the framework of constrained, nonlinear optimization problems, which is an improvement on existing formulations that deal with either unconstrained nonlinear formulations or constrained linear formulations

A Closer Look at Drawbacks of Minimizing Weighted Sums of Objectives for Pareto Set Generation in Multicriteria Optimization Problems

A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case. Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this occurrence. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves

A Protective Role of Arecoline Hydrobromide in Experimentally Induced Male Diabetic Rats

Objectives. Arecoline, the most potent and abundant alkaloid of betel nut, causes elevation of serum testosterone and androgen receptor expression in rat prostate, in addition to increase in serum insulin levels in rats, leading to insulin resistance and type 2 diabetes-like conditions. This study investigated the role of arecoline on the reproductive status of experimentally induced type 1 diabetic rats. Methods. Changes in the cellular architecture were analyzed by transmission electron microscopy. Blood glucose, serum insulin, testosterone, FSH, and LH were assayed. Fructose content of the coagulating gland and sialic acid content of the seminal vesicles were also analyzed. Results. Arecoline treatment for 10 days at a dose of 10 mg/kg of body weight markedly facilitated β-cell regeneration and reversed testicular and sex accessory dysfunctions by increasing the levels of serum insulin and gonadotropins in type 1 diabetic rats. Critical genes related to β-cell regeneration, such as pancreatic and duodenal homeobox 1 (pdx-1) and glucose transporter 2 (GLUT-2), were found to be activated by arecoline at the protein level. Conclusion. It can thus be suggested that arecoline is effective in ameliorating the detrimental effects caused by insulin deficiency on gonadal and male sex accessories in rats with type 1 diabetes

Incidence, risk factors, clinico-microbiological profile, change in ventilator settings needed and outcome of 135 ventilator associated pneumonia cases in pediatric intensive care unit (PICU) of a tertiary care centre in Eastern India

Introduction: Ventilator associated pneumonia (VAP) is the second most common nosocomial infection diagnosed in mechanically ventilated patients with incidence of 20-36%, mainly caused by Gram-negative organisms in our country. Decrease in PaO2/FIO2 (arterial oxygen tension/fractional inspired oxygen) is an early marker of VAP. Impaired consciousness, re-intubation and continuous sedation are the most important risk factors of VAP. We aimed to study the incidence, risk factors, clinico-microbiological profile, change in ventilator settings needed and outcome of VAP in the pediatric intensive care unit (PICU) of a tertiary care centre in Eastern India. Methods: This retrospective, observational study was conducted from January 2015 to June 2017, including 300 patients. We diagnosed VAP using Centre for Disease Control and Prevention (CDC) criteria and analysed the data using the Statistical Package for Social Sciences (SPSS®) version 20.0. Results: Incidence of VAP was 45%, with higher incidence in infants with prolonged ventilation, use of continuous sedation and H2 blockers, re-intubation, presence of genetic syndromes and impaired consciousness. Gram-negative organisms (94%) (P. aeruginosa [45.93%], K. pneumoniae [25.18%], E. coli [14.81%], Acinetobacter spp. [8.14%]) outnumbered Gram-positive organisms (6%) (S. aureus [2.96%], Enterococcus spp. [2.22%] and S. pneumoniae [0.7%]). Resistance to common antibiotics was found in many cases. Multivariate analysis identified nasogastric tube feeding (adjusted odds ratio [OR] = 1.88; 95% CI = 0.8-2.3), use of H2-blockers (adjusted OR = 2.04; 95% CI = 0.51-4.5), use of continuous sedation (adjusted OR = 2.779; 95% CI = 0.7-4.9), re-intubation (adjusted OR = 4.861; 95% CI = 1.6-17.8) and duration of ventilation > 1 week (adjusted OR = 5; 95% CI = 0.7-6.3) as the risk factors for VAP. Purulent tracheal secretions (p < 0.0001), positive tracheal aspirate culture (p < 0.0001) and a suggestive chest radiograph (p < 0.0001) were the strongest predictors of development of VAP. The PaO2/FIO2 ratio was lower in the VAP group in all the three points of comparison but was not significant. The tidal volumes, peak and mean pressures, positive end-expiratory pressures (PEEP) and FIO2 were higher in VAP patients both on days 3 and 5 of ventilation as compared to non-VAP patients but the differences were not statistically significant. Duration of PICU stay (16.5 ± 10.1 days) and mortality (53.3%) was higher in VAP patients compared to non-VAP patients (11.5 ± 9.2 days and 40.6%). Conclusion: Identifying and minimizing the risk factors and proper choice of antibiotics as per sensitivity would improve outcome. Characteristics and parameters of mechanical ventilation were not influenced by the development of VAP. The variables of ventilation would not be sensitive for diagnosing VAP and clinical, radiological and microbiological criteria remain the tools for diagnosing VAP