Separable Convex Optimization with Nested Lower and Upper Constraints

We study a convex resource allocation problem in which lower and upper bounds are imposed on partial sums of allocations. This model is linked to a large range of applications, including production planning, speed optimization, stratified sampling, support vector machines, portfolio management, and telecommunications. We propose an efficient gradient-free divide-and-conquer algorithm, which uses monotonicity arguments to generate valid bounds from the recursive calls, and eliminate linking constraints based on the information from sub-problems. This algorithm does not need strict convexity or differentiability. It produces an $\epsilon$-approximate solution for the continuous problem in $\mathcal{O}(n \log m \log \frac{n B}{\epsilon})$ time and an integer solution in $\mathcal{O}(n \log m \log B)$ time, where $n$ is the number of decision variables, $m$ is the number of constraints, and $B$ is the resource bound. A complexity of $\mathcal{O}(n \log m)$ is also achieved for the linear and quadratic cases. These are the best complexities known to date for this important problem class. Our experimental analyses confirm the good performance of the method, which produces optimal solutions for problems with up to 1,000,000 variables in a few seconds. Promising applications to the support vector ordinal regression problem are also investigated

A crop-land allocation model: A case study in La Rioja, Spain

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.Crop land allocation is a complex process because it requires of consideration of different factors such as ecological, environmental, economical, social, and geographical factors. Crop land allocation has been run by aligning maps with predefined crop site requirements. Geographic Information Systems (GIS) are playing an increasing role in rural planning because of their simplicity and speed of analysis of complex problems. They offer analysis for analyzing spatial and nonspatial attributes of a site. Hence, rural planning has adopted GIS directly, and in this project it has been implemented as the main tool for matching a particular crop to the most suitable areas. La Rioja province has diverse subdivisions of agriculture. Research has found that La Rioja lacks in rural planning, as well as in crop land allocation. Therefore, crop land allocation has been implemented to find out benefits of GIS rural planning. The crop land allocation applied in La Rioja province. The application introduced in this thesis proves that GIS has an invaluable role in the development of rural planning and it opens the door for further GIS applications in this field

Fair Division with a Secretive Agent

We study classic fair-division problems in a partial information setting. This paper respectively addresses fair division of rent, cake, and indivisible goods among agents with cardinal preferences. We will show that, for all of these settings and under appropriate valuations, a fair (or an approximately fair) division among n agents can be efficiently computed using only the valuations of n-1 agents. The nth (secretive) agent can make an arbitrary selection after the division has been proposed and, irrespective of her choice, the computed division will admit an overall fair allocation. For the rent-division setting we prove that the (well-behaved) utilities of n-1 agents suffice to find a rent division among n rooms such that, for every possible room selection of the secretive agent, there exists an allocation (of the remaining n-1 rooms among the n-1 agents) which ensures overall envy freeness (fairness). We complement this existential result by developing a polynomial-time algorithm that finds such a fair rent division under quasilinear utilities. In this partial information setting, we also develop efficient algorithms to compute allocations that are envy-free up to one good (EF1) and epsilon-approximate envy free. These two notions of fairness are applicable in the context of indivisible goods and divisible goods (cake cutting), respectively. This work also addresses fairness in terms of proportionality and maximin shares. Our key result here is an efficient algorithm that, even with a secretive agent, finds a 1/19-approximate maximin fair allocation (of indivisible goods) under submodular valuations of the non-secretive agents. One of the main technical contributions of this paper is the development of novel connections between different fair-division paradigms, e.g., we use our existential results for envy-free rent-division to develop an efficient EF1 algorithm.Comment: 27 page

What is the impact of Information Systems on democracy promotion and the role in decision-making process

Dissertation presented as the partial requirement for obtaining a Master's degree in Information Management, specialization in Information Systems and Technologies ManagementThis study aims to contribute to a better understanding of modern democracy and how democracy can be shaped by information systems solutions. We discuss the role of information systems and social media in democratic activities and how information systems can be a part of core democratic processes and contribute to finding solutions for some of the problems democracies face today. The main question being: how is democracy fostered by the introduction of information systems and the existing information systems platforms today? Several common problems of democracies will be identified, analyzed and paired with relevant information systems platforms or solutions resulting in a conceptual framework that nations can use to improve their democratic processes. Areas identified as relevant for the study are direct democracy using existing technological solutions, collaborative democracy, which would allow citizens to increase participation in the creation of laws, the allocation of budgets and online voting. Although it might not be possible to provide an exhaustive listing of all existing solution, due to the rapidly evolving nature of the information systems field, several existing solutions already provide interesting opportunities for the improvement of current democratic processes and if there was a wider adoption of these technologies it would improve the participation of citizens and reduce the increasing percentage of alienated citizens that abstain from taking part in the democratic process of their countries

Scheduling with Fuzzy Methods

Nowadays, manufacturing industries -- driven by fierce competition and rising customer requirements -- are forced to produce a broader range of individual products of rising quality at the same (or preferably lower) cost. Meeting these demands implies an even more complex production process and thus also an appropriately increasing request to its scheduling. Aggravatingly, vagueness of scheduling parameters -- such as times and conditions -- are often inherent in the production process. In addition, the search for an optimal schedule normally leads to very difficult problems (NP-hard problems in the complexity theoretical sense), which cannot be solved effciently. With the intent to minimize these problems, the introduced heuristic method combines standard scheduling methods with fuzzy methods to get a nearly optimal schedule within an appropriate time considering vagueness adequately

2009-10 statistics derived from ILR data for the monitoring and allocation of funding in FECs

"This document describes: how we used 2009-10 Data Service learner data to inform 2011-12 funding allocations how we used 2009-10 learner data to monitor returns made to HEFCE the responses required from colleges to these monitoring processes." - Page 2

Application of Market Models to Network Equilibrium Problems

We present a general two-side market model with divisible commodities and price functions of participants. A general existence result on unbounded sets is obtained from its variational inequality re-formulation. We describe an extension of the network flow equilibrium problem with elastic demands and a new equilibrium type model for resource allocation problems in wireless communication networks, which appear to be particular cases of the general market model. This enables us to obtain new existence results for these models as some adjustments of that for the market model. Under certain additional conditions the general market model can be reduced to a decomposable optimization problem where the goal function is the sum of two functions and one of them is convex separable, whereas the feasible set is the corresponding Cartesian product. We discuss some versions of the partial linearization method, which can be applied to these network equilibrium problems.Comment: 18 pages, 3 table