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In data envelopment analysis (DEA) literature, the returns to scale (RTS) of an inefficient decision making unit (DMU) is determined at its projected point on the efficient frontier. Under the occurrences of multiple projection points,…
In data envelopment model (DEA), while either the most or least distance based frameworks can be implemented for targeting, the latter is often more relevant than the former from a managerial point of view due to easy attainability of the…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…
Data envelopment analysis (DEA) is one of the most commonly used methods to estimate the returns to scale (RTS) of the public sector (e.g., research institutions). Existing studies are all based on the traditional definition of RTS in…
Models incorporating uncertain inputs, such as random forces or material parameters, have been of increasing interest in PDE-constrained optimization. In this paper, we focus on the efficient numerical minimization of a convex and smooth…
Given a stochastic dynamical system modelled via stochastic differential equations (SDEs), we evaluate the safety of the system through characterizations of its exit time moments. We lift the (possibly nonlinear) dynamics into the space of…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss). Two types of FBS{\Delta}Ss are investigated. The first one is described by a partially…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
In this paper, we study the maximum principle for stochastic optimal control problems of forward-backward stochastic difference systems (FBS{\Delta}Ss) where the uncertainty is modeled by a discrete time, finite state process, rather than…
Distribution system state estimation (DSSE) is an essential tool for operation of distribution networks, the results of which enables the operator to have a thorough observation of the system. Thus, most distribution management systems…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Minimax optimization problems have attracted a lot of attention over the past few years, with applications ranging from economics to machine learning. While advanced optimization methods exist for such problems, characterizing their…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
Mesh degeneration is a bottleneck for fluid-structure interaction (FSI) simulations and for shape optimization via the method of mappings. In both cases, an appropriate mesh motion technique is required. The choice is typically based on…
The characteristic feature of the discrete scale invariant (DSI) processes is the invariance of their finite dimensional distributions by dilation for certain scaling factor. DSI process with piecewise linear drift and stationary increments…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
The exciting field of stretchable electronics (SE) promises numerous novel applications, particularly in-body and medical diagnostics devices. However, future advanced SE miniature devices will require high-density, extremely stretchable…
High-dimensional Kronecker-structured estimation faces a conflict between non-convex scaling ambiguities and statistical robustness. The arbitrary factor scaling distorts gradient magnitudes, rendering standard fixed-threshold robust…
Fast power system state estimation (SE) solution is of paramount importance for achieving real-time decision making in power grid operations. Semidefinite programming (SDP) reformulation has been shown effective to obtain the global optimum…