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Formal definition of the reference frame is given. This definition is valid for nonrelativistic and relativistic cases. Proposed definition allows using wide classes of reference frames without restriction to inertial, uniformly accelerated…
Estimating optical flows is one of the most interesting problems in computer vision, which estimates the essential information about pixel-wise displacements between two consecutive images. This work introduces an efficient dual…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
A method is proposed to estimate the velocity field of an unsteady flow using a limited number of flow measurements. The method is based on a non-linear low-dimensional model of the flow and on expanding the velocity field in terms of…
Single-objective black box optimization (also known as zeroth-order optimization) is the process of minimizing a scalar objective $f(x)$, given evaluations at adaptively chosen inputs $x$. In this paper, we consider multi-objective…
Based on the analysis of the velocity gradient tensor, we investigate in this paper the physical interpretation and limitations of four vortex criteria: $\omega$, $Q$, $\varDelta$ and $\lambda_{ci}$, and reveal the actual physical meaning…
In this paper the notion of the rigid frame of reference within special relativity is analysed. Three definitions of rigidity are formulated. By using several examples of non-inertial frames, it is shown that these definitions are not…
We develop an adaptive-metric framework for norm-minimization-based outer approximation algorithms in bounded convex vector optimization. The key idea is to let the scalarization metric vary across iterations while measuring approximation…
Every volumetric velocimetry measurements based on tracer (particles, bubbles, etc.) detection can be strongly influenced by the optical screening phenomenon. It has to be taken into account when the the statistical properties associated to…
We present a new modeling paradigm for optimization that we call random field optimization. Random fields are a powerful modeling abstraction that aims to capture the behavior of random variables that live on infinite-dimensional spaces…
In this paper, we propose a variable metric method for unconstrained multiobjective optimization problems (MOPs). First, a sequence of points is generated using different positive definite matrices in the generic framework. It is proved…
This paper is concerned with objective value performance of the scenario approach for robust convex optimization. A novel method is proposed to derive probabilistic bounds for the objective value from scenario programs with a finite number…
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, such problems are typically tackled…
Let M be an oriented three-dimensional Riemannian manifold. We define a notion of vorticity of local sections of the bundle SO(M) --> M of all its positively oriented orthonormal tangent frames. When M is a space form, we relate the concept…
Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…
We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their…
This article develops a methodology that enables learning an objective function of an optimal control system from incomplete trajectory observations. The objective function is assumed to be a weighted sum of features (or basis functions)…
We give a critical analysis of the conceptual foundations of special relativity. We formulate a simple operational criterion for distinguishing between noninertial and inertial frames which is introduced prior to geometry. We associate the…
To more flexibly balance between exploration and exploitation, a new meta-heuristic method based on Uncertainty Principle concepts is proposed in this paper. UP is is proved effective in multiple branches of science. In the branch of…
We propose a conditional gradient framework for a composite convex minimization template with broad applications. Our approach combines smoothing and homotopy techniques under the CGM framework, and provably achieves the optimal…