相关论文: Phonological Derivation in Optimality Theory
Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…
The inverse potential problem consists in determining the density of the volume potential from measurements outside the sources. Its ill-posedness is due both to the non-uniqueness of the solution and to the instability of the solution with…
The unit-derived method in coding theory is shown to be a unique optimal scheme for constructing and analysing codes. In many cases efficient and practical decoding methods are produced. Codes with efficient decoding algorithms at maximal…
An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy…
This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…
The study of first-order optimization is sensitive to the assumptions made on the objective functions. These assumptions induce complexity classes which play a key role in worst-case analysis, including the fundamental concept of algorithm…
In this paper we consider the minimization of a continuous function that is potentially not differentiable or not twice differentiable on the boundary of the feasible region. By exploiting an interior point technique, we present first- and…
Many theories are formulated as constrained systems. We provide a mechanism that explains the origin of physical states of a constrained system by a process of selection of noiseless subsystems when the system is coupled to an external…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
Optimization algorithms appear in the core calculations of numerous Artificial Intelligence (AI) and Machine Learning methods, as well as Engineering and Business applications. Following recent works on the theoretical deficiencies of AI, a…
Deep Neural Networks (DNNs) outshine alternative function approximators in many settings thanks to their modularity in composing any desired differentiable operator. The formed parametrized functional is then tuned to solve a task at hand…
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…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
One of the basic principles of Approximation Theory is that the quality of approximations increase with the smoothness of the function to be approximated. Functions that are smooth in certain subdomains will have good approximations in…
Concurrent to the rapid progress in the development of neural-network based models in areas like natural language processing and computer vision, the need for creating explanations for the predictions of these black-box models has risen…
We develop aspects of music theory related to harmony, such as scales, chord formation and improvisation from a combinatorial perspective. The goal is to provide a foundation for this subject by deriving the basic structure from a few…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure.…