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.
Results
Showing 1 to 20 of 38 for “"convex relaxation"”.
-
A convex relaxation approach to set-membership identification
… data sequence. Such problems are generally nonconvex and NP-hard. Therefore, standard nonlinear optimization tools can not be used to compute parameter bounds, since they can trap in local minima and, as a consequence, the computed bounds are not guaranteed to contain the true values of …
-
Convex relaxation based locational marginal prices for electricity markets
We propose and analyze semidefinite relaxation-based locational marginal prices (RLMPs) for real and reactive power in electricity markets. Our analysis reveals that when the nonconvex economic dispatch problem has zero duality gap, the RLMPs exhibit properties similar to locational marginal prices …
-
Convex relaxation methods for graphical models : Lagrangian and maximum entropy approaches
… over general graphs. In this thesis, we consider convex optimization methods to address two central problems that commonly arise for graphical models. First, we consider the problem of determining the most probable configuration-also known as the maximum a posteriori (MAP) estimate-of all …
-
Relaxing Topological Barriers in Geometry Processing
… barriers that hinder optimization, leading to nonconvexity, initialization-dependence, and local minima. This thesis explores convex relaxation as a powerful guide and tool for reframing such problems. We bring the tools of semidefinite relaxation to bear on challenging optimization problems in …
-
Unit commitment : tight formulation and pricing
… as generation expansion planning (GEP). The non-convex costs associated with the commitment decisions may also lead to generators' incentive to deviate from the optimal dispatch under locational marginal prices. In this dissertation, we first propose a convex relaxation of UC based on a primal …
-
Low-rank completion and recovery of correlation matrices
… presents the methods of spectral completion and convex relaxation, which have been successfully applied to the particular problem of lowrank completion and recovery of valid correlation matrices. Numerical testing was performed on the classical exponential and noisy Toeplitz parametrisations and, …
-
Collaborative ranking from ordinal data
… thesis presents a matrix factorization inspired, convex relaxation algorithm to collaboratively learn hidden preferences of users through the multinomial logit (MNL) model, a discrete choice model. It also shows that the algorithm is efficient in terms of the number of observations needed.
-
Surpassing Local Optimality in Geometry Processing
… results. We specifically explore the use of convex relaxation, variable augmentation and sum-of-squares programming to target cross-field based quad meshing, hexahedral mesh quality enhancement, and algebraic collision detection. With these tools, we manage to avoid shallower local minima and …
-
Low rank matrix completion
… solve the problem approximately by solving the convex relaxation of the original problem. One particularly popular method is to use nuclear norm (sum of singular values) to approximate the rank of the matrix and formulate the problem as a semidefinite program that can be solved efficiently. In …
-
Improvements in magnetic resonance imaging excitation pulse design
… need to be as short as possible due to spin relaxation, tissue heating, and main field inhomogeneity limitations. When magnetic spins are tilted by only a small amount, pulse transmission may be interpreted as depositing energy in a continuous three-dimensional Fourier-like domain along a …
-
Low rank methods for optimizing clustering
… objective is NP-hard, and even though there is a convex relaxation of the objective, straightforward convex optimization approaches are too expensive for large datasets. We utilize low rank structures in the solution matrix of the convex formulation and use a low-rank factorization of the solution …
-
Linear and nonlinear semidefinite relaxations of some NP-hard problems
Semidefinite relaxation (SDR) is a powerful tool to estimate bounds and obtain approximate solutions for NP-hard problems. This thesis introduces and studies several novel linear and nonlinear semidefinite relaxation models for some NP-hard problems. We first study the semidefinite relaxation of …
-
LOW RANK AND SPARSE MODELING FOR DATA ANALYSIS
… problem is computationally NP-hard, the convex relaxation of original problem is often solved. One popular heuristic method is to use the nuclear norm to approximate the rank of a matrix. Despite the success of nuclear norm minimization in capturing the low intrinsic-dimensionality of …
-
Algorithms for Gibbs states of quantum many-body systems
… asymptotic runtimes. Beyond 1D, using ideas from convex optimization, we design hierarchies of relaxations for observables in thermal states. While quantitative convergence guarantees only apply to restricted settings, we prove a qualitative convergence result in full generality with implications …
-
Approximate Message Passing for Matrix Regression
… For comparison, we propose estimators based on convex relaxation and iterative thresholding, without providing theoretical guarantees. To further improve the performance of AMP algorithms for QGT and pooled data, we introduce the spatially coupled Bernoulli test matrix and an AMP algorithm. We …
-
Sensitivity analysis for nonsmooth dynamic systems
… of nonsmoothness, a variant of McCormick's convex relaxation scheme is developed and implemented for use in global optimization methods. This variant produces twice-continuously differentiable convex underestimators for composite functions, while retaining the advantageous computational …
-
Power and limitations of convex formulations via linear and semidefinite programming lifts
Convex relaxation methods play an important role in mathematical optimization to tackle hard nonconvex problems, and have been applied successfully in many areas of science and engineering. At the heart of such methods lies the question of obtaining a tractable description of the convex hull of a …
-
Advances in Nonconvex and Robust Optimization
Nonconvex optimization presents significant challenges, as identifying the global optimum is often difficult. This thesis introduces novel algorithms to find the exact solution of a broad class of nonconvex optimization problems. The thesis is structured into four parts. In Chapter 2, we propose a …
-
Optimal design and operation of energy polygeneration systems
… problem is a potentially large-scale nonconvex mixed-integer nonlinear program (MINLP) and cannot be solved to global optimality by state-of-the-art global optimization solvers, such as BARON, within a reasonable time. The nonconvex generalized Benders decomposition (NGBD) method can …
-
Computable Performance Analysis of Recovering Signals with Low-dimensional Structures
… I derive bounds on the recovery errors of convex relaxation algorithms in terms of these goodness measures. Using tools from empirical processes and generic chaining, I analytically demonstrate that as long as the number of measurements are relatively large, these goodness measures are …
Page 1 of 2