Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 44 for “"non-convex optimization"”.
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Global Non-Convex Optimization with Integer Variables
Non-convex optimization refers to the process of solving problems whose objective or constraints are non-convex. Historically, this type of problems have been very difficult to solve to global optimality, with traditional solvers often relying on approximate solutions. Bertsimas et al. [1] …
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Topics in non-convex optimization and learning
Non-convex optimization and learning play an important role in data science and machine learning, yet so far they still elude our understanding in many aspects. In this thesis, I study two important aspects of non-convex optimization and learning: Riemannian optimization and deep neural networks. …
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Traversing Rugged Domains: Explorations in Non-convex Optimization Theory and Software
… theoretical and computational frameworks for nonlinear, nonconvex optimization problems in statistics, machine learning, and optimal control. Disciplined Geodesically Convex Programming (DGCP) extends convexity verification to Riemannian manifolds, enabling optimization on curved spaces with …
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Cooperative Game Theory and Non-convex Optimization Analysis of Spectrum Sharing
… interactions in the wireless medium can lead to non-convex problems which have been shown to be NP-hard. Techniques must be developed to tackle the optimization problems that arise from wireless network analysis. In this document we focus on analyzing the spectrum sharing problem from two …
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Applicability of deep learning approaches to non-convex optimization for trajectory-based policy search
Trajectory optimization is a powerful tool for determining good control sequences for actuating dynamical systems. In the past decade, trajectory optimization has been successfully used to train and guide policy search within deep neural networks via optimizing over many trajectories …
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Out-of-equilibrium sampling as a protocol to unveil locally-smooth neural network configurations in non-convex optimization
L'abstract è presente nell'allegato / the abstract is in the attachment
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Stochastic optimization with decisions truncated by random variables and its applications in operations
We study stochastic optimization problems with decisions truncated by random variables and its applications in operations management. The technical difficulty of these problems is that the optimization problem is not convex due to the truncation. We develop a transformation technique to convert the …
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Contraction maps and applications to the analysis of iterative algorithms
… community, and especially machine learning, on non-convex problems, has made non-convex optimization one of the most important and challenging areas of our days. Despite of this increasing interest too little is known from a theoretical point of view. The main reason for this is that the …
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Minimum Variance Benchmark and Performance Assessment for PID Controllers
… variance with the minimum variance (MV) for the non-restricted linear controller. MV describes the most fundamental performance limitation of a system due to time delays or infinite zeros. MV is estimated with-out disturbing the system and just needs the time delay of a process and its …
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An inverse problem framework for reconstruction of phonon properties using solutions of the Boltzmann transport equation
A methodology for reconstructing phonon properties in a solid material, such as the frequency-dependent relaxation time distribution, from thermal spectroscopy experimental results is proposed and extensively validated. The reconstruction is formulated as a non-convex optimization problem whose …
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Learning and optimization in the face of data perturbations
… This is the classic problem of stochastic optimization. There are two key challenges in solving such stochastic optimization problems: 1) the function is often non-convex, making optimization difficult; 2) the distribution is not known exactly, but may be perturbed adversarially or is …
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Optimal GENCO bidding strategy
… dispatch with Combined Cycle units becomes a non-convex optimization problem, which is difficult if not impossible to solve by conventional methods. Several techniques are proposed here: Mixed Integer Linear Programming, a hybrid method, as well as Evolutionary Algorithms. Evolutionary …
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Distributed Training with Heterogeneous Data: Bridging Median- and Mean-Based Algorithms
… study of median-based algorithms for distributed non-convex optimization. Two prominent examples include signSGD with majority vote, an effective approach for communication reduction via 1-bit compression on the local gradients, and medianSGD, an algorithm recently proposed to ensure robustness …
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Branch-and-Price for Prescriptive Contagion Analytics
… contagion problems involve mixed-integer non-convex optimization models with constraints governed by ordinary differential equations, thus combining the challenges of combinatorial optimization, non-linear optimization, and continuous-time system dynamics. This thesis develops a …
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Decentralized signal processing systems with conservation principles
… a framework for designing fixed-point and optimization algorithms realized as asynchronous, distributed signal processing systems is developed with an emphasis on the system's stability, robustness, and variational properties. These systems are formed by connecting basic modules together …
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The Distance to Uncontrollability via Linear Matrix Inequalities
… of the distance to uncontrollability leads to a non-convex optimization problem in two variables. In 2000 Gu proposed the first polynomial time algorithm to compute this distance. This algorithm relies heavily on efficient eigenvalue solvers. In this work we examine two alternative algorithms …
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Making Sense of Training Large AI Models
Today, one of the most impressive applications of optimization is the training of large AI models. But currently such models are trained with ad-hoc heuristics at a very large computational cost, mainly due to lack of understanding of their working mechanisms. In this thesis, we conduct a …
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Robustness Verification and Optimization of Nonlinear Systems
Nonlinear systems allow us to describe and analyze physical and virtual systems, including dynamical systems, power grids, robots, and neural networks. The problems involving nonlinearity pose challenges in providing safety guarantees and robustness in the presence of uncertainty. This thesis …
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Joint relay beamforming and transceiver processing in multiuser relay network
… to pre-defined SINR requirements. The resulting non-convex optimization problem is solved by ordinary semi-definite relaxation (SDR) and separable SDR approaches. Compared to conventional rank-one scheme, proposed rank-two methods provide one more degree of freedom in optimal solution, and have …
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