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To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…
This paper proposes two efficient approximation methods to solve high-dimensional fully nonlinear partial differential equations (NPDEs) and second-order backward stochastic differential equations (2BSDEs), where such high-dimensional fully…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…
Gradient-based methods are well-suited for derivative-free optimization (DFO), where finite-difference (FD) estimates are commonly used as gradient surrogates. Traditional stochastic approximation methods, such as Kiefer-Wolfowitz (KW) and…
The predictive quality of machine learning models is typically measured in terms of their (approximate) expected prediction error or the so-called Area Under the Curve (AUC) for a particular data distribution. However, when the models are…
A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…
We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an…
This thesis presents new mathematical algorithms for the numerical solution of a mathematical problem class called \emph{dynamic optimization problems}. These are mathematical optimization problems, i.e., problems in which numbers are…
Variational regularization techniques are dominant in the field of mathematical imaging. A drawback of these techniques is that they are dependent on a number of parameters which have to be set by the user. A by now common strategy to…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
Bilevel programming has recently received attention in the literature due to its wide range of applications, including reinforcement learning and hyper-parameter optimization. However, it is widely assumed that the underlying bilevel…
Circumcentered techniques have been shown to significantly accelerate projection-based methods for convex feasibility problems. Motivated by this success, we propose two direct methods with circumcenter acceleration for solving variational…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
Divide and Conquer (DC) is conceptually well suited to high-dimensional optimization by decomposing a problem into multiple small-scale sub-problems. However, appealing performance can be seldom observed when the sub-problems are…
This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice…
Finite-dimensional dissipative dynamical systems with multiple time-scales are obtained when modeling chemical reaction kinetics with ordinary differential equations. Such stiff systems are computationally hard to solve and therefore,…
We consider a higher-order Milstein scheme for stochastic partial differential equations with trace class noise which fulfill a certain commutativity condition. A novel technique to generally improve the order of convergence of Taylor…
Both bilevel and robust optimization are established fields of mathematical optimization and operations research. However, only until recently, the similarities in their mathematical structure has neither been studied theoretically nor…