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Traditional mathematical programming solvers require long computational times to solve constrained minimization problems of complex and large-scale physical systems. Therefore, these problems are often transformed into unconstrained ones,…
Many traditional signal recovery approaches can behave well basing on the penalized likelihood. However, they have to meet with the difficulty in the selection of hyperparameters or tuning parameters in the penalties. In this article, we…
We present the first sub-quadratic time algorithm that with high probability correctly reconstructs phylogenetic trees for short sequences generated by a Markov model of evolution. Due to rapid expansion in sequence databases, such very…
We consider a convex optimization problem with many linear inequality constraints. To deal with a large number of constraints, we provide a penalty reformulation of the problem, where the penalty is a variant of the one-sided Huber loss…
Mobile robotic platforms are an indispensable tool for various scientific and industrial applications. Robots are used to undertake missions whose execution is constrained by various factors, such as the allocated time or their remaining…
Current algorithms used to put a lattice gauge configuration into Landau gauge either suffer from the problem of critical slowing-down or involve an additional computational expense to overcome it. Evolutionary Algorithms (EAs), which have…
The starting point for this work is a static macroscopic model for a high-contrast layered material in single-slip finite crystal plasticity, identified in [Christowiak & Kreisbeck, Calc. Var. PDE (2017)] as a homogenization limit via…
The convergence rate of stochastic gradient search is analyzed in this paper. Using arguments based on differential geometry and Lojasiewicz inequalities, tight bounds on the convergence rate of general stochastic gradient algorithms are…
In this paper, we analyze the local convergence rate of optimistic mirror descent methods in stochastic variational inequalities, a class of optimization problems with important applications to learning theory and machine learning. Our…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
In many global Optimization Problems, it is required to evaluate a global point (min or max) in large space that calculation effort is very high. In this paper is presented new approach for optimization problem with subdivision labeling…
When we try to solve a system of linear equations, we can consider a simple iterative algorithm in which an equation including only one variable is chosen at each step, and the variable is fixed to the value satisfying the equation. The…
The NSGA-III algorithm relies on uniformly distributed reference points to promote diversity in many-objective optimization problems. However, this strategy may underperform when facing irregular Pareto fronts, where certain vectors remain…
This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and…
We propose a new policy gradient method, named homotopic policy mirror descent (HPMD), for solving discounted, infinite horizon MDPs with finite state and action spaces. HPMD performs a mirror descent type policy update with an additional…
During recent years the interest of optimization and machine learning communities in high-probability convergence of stochastic optimization methods has been growing. One of the main reasons for this is that high-probability complexity…
This paper proposes a new method for hyperparameter optimization (HPO) that balances exploration and exploitation. While evolutionary algorithms (EAs) show promise in HPO, they often struggle with effective exploitation. To address this, we…
The performance of Newton-Raphson, Levenberg-Marquardt, Damped Newton-Raphson and genetic algorithms are investigated for the estimation of induction motor equivalent circuit parameters from commonly available manufacturer data. A new…
We propose Hybridizable Discontinuous Galerkin (HDG) methods for solving the frequency-domain Maxwell's equations coupled to the Nonlocal Hydrodynamic Drude (NHD) and Generalized Nonlocal Optical Response (GNOR) models, which are employed…