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We develop an efficient stochastic variance reduced gradient descent algorithm to solve the affine rank minimization problem consists of finding a matrix of minimum rank from linear measurements. The proposed algorithm as a stochastic…
We propose randomized subspace gradient methods for high-dimensional constrained optimization. While there have been similarly purposed studies on unconstrained optimization problems, there have been few on constrained optimization problems…
In this work we propose an adaptive multilevel version of subset simulation to estimate the probability of rare events for complex physical systems. Given a sequence of nested failure domains of increasing size, the rare event probability…
In this work we focus on the problem of minimizing the sum of convex cost functions in a distributed fashion over a peer-to-peer network. In particular, we are interested in the case in which communications between nodes are prone to…
This work is devoted to the study of a posteriori error estimation and adaptivity in parabolic problems with a particular focus on spatial discontinuous Galerkin (dG) discretisations. We begin by deriving an a posteriori error estimator for…
Adaptive sampling algorithms are modern and efficient methods that dynamically adjust the sample size throughout the optimization process. However, they may encounter difficulties in risk-averse settings, particularly due to the challenge…
Vortex-induced vibration (VIV) manifests its destructiveness on marine risers in deep-water oil and gas development. Many types of riser fairings are employed in the practical applications of ocean engineering due to their effectiveness in…
Dampers are devices that reduce delay jitter in the context of time-sensitive networks, by delaying packets for the amount written in packet headers. Jitter reduction is required by some real-time applications; beyond this, dampers have the…
This paper presents an optimization-based receding horizon trajectory planning algorithm for dynamical systems operating in unstructured and cluttered environments. The proposed approach is a two-step procedure that uses a motion planning…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
The goal of this thesis is to study the compression problems arising in distributed computing systematically. In the first part of the thesis, we study gradient compression for distributed first-order optimization. We begin by establishing…
We give a method for proactively identifying small, plausible shifts in distribution which lead to large differences in model performance. These shifts are defined via parametric changes in the causal mechanisms of observed variables, where…
Bilevel optimization is a key framework in hierarchical decision-making, where one problem is embedded within the constraints of another. In this work, we propose a control-theoretic approach to solving bilevel optimization problems. Our…
Fault tolerant algorithms for the numerical approximation of elliptic partial differential equations on modern supercomputers play a more and more important role in the future design of exa-scale enabled iterative solvers. Here, we combine…
The work explores a specific scenario for structural computational optimization based on the following elements: (a) a relaxed optimization setting considering the ersatz (bi-material) approximation, (b) a treatment based on a nonsmoothed…
This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…
Recent developments in the field of computational modeling of fracture have opened up possibilities for designing structures against failure. A special case, called interfacial fracture or delamination, can occur in loaded composite…
This work presents a rigorous mathematical formulation for topology optimization of a macrostructure undergoing ductile failure. The prediction of ductile solid materials which exhibit dominant plastic deformation is an intriguingly…
Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the…
Scalable algorithms of posterior approximation allow Bayesian nonparametrics such as Dirichlet process mixture to scale up to larger dataset at fractional cost. Recent algorithms, notably the stochastic variational inference performs local…