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We present a fully polynomial time approximation scheme (FPTAS) for optimizing a very general class of non-linear functions of low rank over a polytope. Our approximation scheme relies on constructing an approximate Pareto-optimal front of the linear functions which constitute the given low-rank function. In contrast to existing results in the literature,(More)
We present a three-dimensional offline path planner for Unmanned Aerial Vehicles (UAVs) using a multiobjective optimization procedure for simultaneous optimization of two conflicting goals: (i) minimization of the length of overall path and (ii) maxi-mization of the margin of safety from ground obstacles. This method is different from 1 existing(More)
The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract In this paper, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination of more than one function. Examples of such problems include(More)
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Abstract— In this paper, we present a new paradigm of searching optimal(More)
This thesis presents efficient algorithms that give optimal or near-optimal solutions for problems with non-linear objective functions that arise in discrete, continuous and robust optimization. First, we present a general framework for designing approximation schemes for combinatorial optimization problems in which the objective function is a combination(More)
We consider the problem of appointment scheduling in a robust optimization framework. The appointment scheduling problem arises in many service operations, for example health care. For each job, we are given its minimum and maximum possible execution times. The objective is to find an appointment schedule for which the cost in the worst case scenario of the(More)
In the last three decades, with rapid advancements in the hardware and software industry, a large number of commercial and free open source languages and software have evolved. Many of these are Very High Level Languages (VHLLs) which can be easily used for scientific computing purposes such as algorithm testing and engineering computations. However, this(More)
Games are an effective modeling tool for systems involving interaction with the environment. Situations where there are two players having conflicting goals as well as a random agent are best depicted by stochastic games. This paper deals mainly with stochastic games with ω-regular objectives, specifically Büchi winning condition. We present a sub-quadratic(More)