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 31 for “"Interior-point methods"”.
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Scaling and Interior Point Methods in Optimization
… four algorithms that use either scaling or interior point methods for convex optimization problems; two of the algorithms use both.
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Inexact interior point methods for constrained convex quadratic optimization problems
Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2022-11-15 without embargo terms
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Interior Point Methods and Kernel Functions of a Linear Programming Problem
In this thesis the Interior -- Point Method (IPM) for Linear Programming problem (LP) that is based on the generic kernel function is considered. The complexity (in terms of iteration bounds) of the algorithm is first analyzed for a class of kernel functions defined by (3-1). This class is fairly …
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A modified augmented Lagrangian merit function, and Q-superlinear characterization results for primal-dual Quasi-Newton interior-point method for nonlinear programming
Two classes of primal-dual interior-point methods for nonlinear programming are studied. The first class corresponds to a path-following Newton method formulated in terms of the nonnegative variables rather than all primal and dual variables. The centrality condition is a relaxation of the …
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Perspectives on Geometry and Optimization: from Measures to Neural Networks
… geometrical aspects of matrix completion, interior point methods, unbalanced optimal transport, and neural network training. We use these examples to illustrate four ways in which geometry plays key yet fundamentally different roles in optimization. The first part explores the benign …
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Using interior point algorithms for the solution of linear programs with special structural features
… of most research was shifted to the field of interior point methods. The present work is concerned with investigating and efficiently implementing the latest techniques in this field taking sparsity into account. The performance of these implementations on different classes of LP problems is …
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A Conic Quadratic Interior-Point Method for a Class of Stratified Sampling Problems
… of this thesis is to numerically test two interior point methods on the stratified sampling problem. First, a homogeneous conic quadratic interior point method was used to solve the stratified sampling problem as a reformulated conic quadratic problem Then, a nonlinear homogeneous interior …
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Techniques for handling nonsymmetric cones in interior point algorithms
… are amenable to highly efficient primal-dual interior point methods, which are implemented by many popular off-the-shelf conic solvers. On the other hand, many useful conic sets cannot be modeled exactly or can be modeled more efficiently using cones that are not symmetric. Algorithms for …
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Preconditioning of Karush--Kuhn--Tucker Systems arising in Optimal Control Problems
… (KKT) optimality conditions or in interior--point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the purpose of this thesis to investigate systems arising from general quadratic programming problems, but to study systems arising in linear quadratic …
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Robust stability and contraction analysis of nonlinear systems via semidefinite optimization
… solved numerically with computationally-effcient interior-point methods. Many of the first LMI-based stability formulations applied to linear systems and the class of nonlinear systems representable as an interconnection of a linear system with bounded uncertainty blocks. Recently, stability and …
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Computational issues and related mathematics of an exponential annealing homotropy for conic optimization
… convex optimization. In particular, inspired by interior-point methods, we propose modifying the hit-and-run random walk to bias iterates away from the boundary of the feasible region and show that this approach yields a substantial reduction in computational cost. We perform computational …
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Interior point and outer approximation methods for conic optimization
… the generality and practical performance of (i) interior point methods for continuous conic problems and (ii) outer approximation methods for mixed-integer conic problems. We implement our algorithms in extensible open source solvers accessible through the convenient modeling language JuMP. From …
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Flows, Submodularity, Sparsity, and Beyond: Continuous Optimization Insights for Discrete Problems
… main contribution is to show that the runtime of interior point methods is closely connected to spectral connectivity notions in the underlying graph, such as electrical conductance and effective resistance. We explore these connections along two orthogonal directions: Making manual interventions …
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Model Reduction Using Semidefinite Programming
In this thesis model reduction methods for linear time invariant systems are investigated. The reduced models are computed using semidefinite programming. Two ways of imposing the stability constraint are considered. However, both approaches add a positivity constraint to the program. The input to …
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Essays on variational inequalities and competitive supply chain models
… thesis we combine ideas from cutting plane and interior point methods to solve variational inequality problems efficiently. In particular, we introduce "smarter" cuts into two general methods for solving these problems. These cuts utilize second order information on the problem through the use …
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The Distance to Uncontrollability via Linear Matrix Inequalities
… problems are solved using primal-dual-interior point methods that retain positive semidefiniteness at each iteration. Numerical results are presented to compare the three algorithms for a number of benchmark examples. In addition, we also consider a system that results from a finite …
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A Feasibility Problem Approach For Reachable Set Approximation
… to check the reachability of discrete grid points of a reachable set which is approximated via an equidistant grid discretization. We use the concept of interior point methods to develop an algorithm for solving many feasibility problems synchronously. Through a suitable problem definition …
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A Comparison of Methods for Seriation and Unidimensional Scaling of Asymmetric Proximity Data
… handle in an optimal way. Unidimensional scaling methods have the ability to attain precise coordinate estimates of the objects. The results of this study show that coordinate estimation methods allow for global optimization of larger matrices than seriation, and can be more accurate. Coordinate …
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Computation of upper and lower bounds in limit analysis using second-order cone programming and mesh adaptivity
… from solving an infinite dimensional saddle point problem, where the internal work rate is maximized over an admissible set of stresses -defined by a yield condition- and minimized over the linear space of kinematically admissible velocities for which the external work rate equals the unity. …
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Non-interior path-following methods for complementarity problems
… of its excellent numerical performance, non-interior path following methods (also called smoothing methods) have become an important class of methods for solving complementarity problems. However, no rate of convergence results are available for these methods. In this thesis, we bridge this …
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