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 33 for “"Variational inequality"”.
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On the analysis of stochastic optimization and variational inequality problems
… problem classes: [(1)] Convex Nash games; [(2)] Variational inequality problems and complementarity problems; [(3)] Hierarchical risk management problems in financial networks. Accordingly, this dissertation considers the analysis of a broad class of stochastic optimization and variational …
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On the resolution of misspecification in stochastic optimization, variational inequality, and game-theoretic problems
… problems have been either sequential or direct variational approaches. In the case of the former, this entails the following steps: (i) a solution to the learning problem for parameters is first obtained; and (ii) a solution is obtained to the associated parametrized computational problem by …
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Solving asymmetric variational inequality problems and systems of equations with generalized nonlinear programming algorithms
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1985.
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Non-smooth dynamics and sensitivity analysis of multibody systems with clearances and friction in differential variational inequality framework
… dynamics approach results in a differential variational inequality (DVI) problem with complementarity constraints. This work provides a comprehensive re view of key contributions in the field of non-smooth dynamics and describes a framework to implement the non-smooth dynamics approach to …
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Estimates for the rate of convergence of finite element approximations of the solution of a time-dependent variational inequality
… to the solution of a time-dependent variational inequality. The two types of approximations considered are the following: 1. Semi-discrete approximations, in which only the spatial domain is discretised by finite elements; 2. fully discrete approximations, in which the spatial domain …
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A motion of freely oscillating droplet of a yield stress fluid: analysis and numerical studies
… fluid with free surface. In this thesis, a variational inequality formulation is deduced for the problem of yield stress fluid dynamics with a free surface. The free surface is assumed to evolve with a normal velocity of the flow. We also consider capillary forces acting along the free …
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A bi-level programming approach for the shipper-carrier network problem
… optimization problem or as a variational inequality problem,depending on whether the oligopolistic carriers choose to collude orcompete with each other in their pricing decision. The shippers' decisionbehavior is defined by the spatial price equilibrium principle. Forthe …
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Game theoretic formulations and solution methods for microeconomic market models
… several of these problems from the standpoint of variational inequality theory. In addition to proving theoretical results about problem properties, important microeconomic implications are discussed when applicable. The individual chapters of this work focus on: • equilibrium existence for …
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Stochastic approximation schemes for stochastic optimization and variational problems: adaptive steplengths, smoothing, and regularization
… Nash games and more recently stochastic variational inequalities. Several challenges arise in the development of SA schemes. First, little guidance is provided on the choice of the steplength sequence. Second, most variants of these schemes in optimization require differentiability of the …
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Distributed algorithms for networked multi-agent systems: optimization and competition
… problems to addressing the solution of variational inequality problems. Two key complicating characteristics of multi-agent systems are the following: (i) the lack of availability of system-wide information at any given location; and (ii) the absence of any central coordinator. These …
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Stochastic numerical approximation approaches for estimation of traffic volume under travel demand uncertainties
… user equilibrium problem solved using the variational inequality method, under demand uncertainties modeled as random inputs. Smolyak sparse grid interpolation technique was successfully applied to the problem and compared to Monte Carlo sampling. Performance of constructed interpolant was …
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Results on the fixed points of multifunctions with applications to problems in optimization and equilibrium theory
… to obtain existence results for several types of variational inequality problems. In particular, extensions of Eaves' ""basic theorem of complementarity"" are given. Next, some outstanding questions are settled regarding the $\alpha$-core of an exchange economy. It is shown that an exchange …
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Nash equilibrium problems in power markets and product design: Analysis and algorithms
… by a solvable monotone single-valued variational inequality. If the risk-measures are generalized to allow for strategic interactions, then the characterization is through a multi-valued variational inequality. Both this object and its single-valued counterpart, arising from the …
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A pure-jump market-making model for high-frequency trading
… using classical Hamilton-Jacobi-Bellman quasi-variational inequality (HJBQVI), so we extend the framework of constrained forward backward stochastic differential equation (CFBSDE) to solve our optimal control problem.</p>
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Robust optimization, game theory, and variational inequalities
… to the notion of equilibrium: the nominal variational inequality (VI) problem over a polyhedron, the finite game under payoff uncertainty, and the network design problem under demand uncertainty. In the first part of the thesis, we demonstrate that the nominal VI problem is in fact a …
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Theory and Algorithms for Nonlinear Optimization and Variational Inequalities
… introduce and analyze a generalized parametric variational inequality problem $PVI(E, T, C, \psi$, Z) in locally convex Hausdorff topological vector spaces. Based on Nikaido's coincidence theorem, we establish several general existence theorems, even without requiring convexity nor …
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Bregman Augmented Lagrangian Method: Convergence, acceleration, and applications in reinforcement learning
… show that the algorithm can also be applied to variational inequality problems with convex constraints, and fully characterize the iteration complexity of the algorithm derived from the inexact version of BALM. Furthermore, we develop, for the first time, an accelerated Bregman proximal point …
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Essays on variational inequalities and competitive supply chain models
… 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 of a gap function. We establish …
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Structure-Preserving High Performance Computational Methods for Transport in Porous Media
… computational framework that can ensure variationally consistent non-negative concentrations for large-scale anisotropic diffusion problems like Chromium remediation in the Sandia Canyon. The predicted computational performance of the proposed framework is based on a “perfect-cache” …
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Robust Control for Hybrid, Nonlinear Systems
… system) with solutions of the appropriate variational inequality (VI). We show that the stopping-time rule can be obtained by solving the VI in the viscosity sense. It also happens that a positive definite supersolution of the VI can be used for stability analysis. We also show how to solve …
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