Continuous Optimization

Protected: Confidence Region Methods in Sequential Optimization in Machine Learning

Confidence region methods (dogleg method, norm constraint, model function optimization, approximate solution of subproblems, modified Newton method, search direction, globally optimal solution, Newton method, steepest descent method, confidence region radius, confidence region, descent direction, step width) in continuous optimization in machine learning used for digital transformation, artificial intelligence, machine learning tasks.

2023.03.20

アルゴリズム:Algorithmsグラフ理論スパースモデリング幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Quasi-Newton Methods as Sequential Optimization in Machine Learning (2)Quasi-Newton Methods with Memory Restriction

Quasi-Newton method with memory restriction (sparse clique factorization, sparse clique factorization, chordal graph, sparsity, secant condition, sparse Hessian matrix, DFP formula, BFGS formula, KL divergence, quasi-Newton method, maximal clique, positive definite matrix, positive definite matrix completion, positive define matrix composition, graph triangulation, complete subgraph, clique, Hessian matrix, triple diagonal matrix Hestenes-Stiefel method, L-BFGS method)

2023.03.07

アルゴリズム:Algorithmsスパースモデリング微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra集合論:Set theory

Protected: Quasi-Newton Method as Sequential Optimization in Machine Learning(1) Algorithm Overview

Quasi-Newton methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks (BFGS formulas, Lagrange multipliers, optimality conditions, convex optimization problems, KL divergence minimization, equality constrained optimization problems, DFG formulas, positive definite matrices, geometric structures, secant conditions, update laws for quasi-Newton methods, Hesse matrices, optimization algorithms, search directions, Newton methods)

2023.02.21

アルゴリズム:Algorithms微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra集合論:Set theory

Protected: Conjugate gradient and nonlinear conjugate gradient methods as continuous optimization in machine learning

Conjugate gradient methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks (moment method, nonlinear conjugate gradient method, search direction, inertia term, Polak-Ribiere method, linear search, Wolf condition, Dai-Yuan method, strong Wolf condition, Fletcher-Reeves method, global convergence, Newton method, rapid descent method, Hesse matrix, convex quadratic function, conjugate gradient method, minimum eigenvalue, maximum eigenvalue, affine subspace, conjugate direction method, coordinate descent method)

2023.02.07

アルゴリズム:Algorithms幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Gauss-Newton and natural gradient methods as continuous optimization for machine learning

Gauss-Newton and natural gradient methods as continuous machine learning optimization for digital transformation, artificial intelligence, and machine learning tasks Sherman-Morrison formula, one rank update, Fisher information matrix, regularity condition, estimation error, online learning, natural gradient method, Newton method, search direction, steepest descent method, statistical asymptotic theory, parameter space, geometric structure, Hesse matrix, positive definiteness, Hellinger distance, Schwarz inequality, Euclidean distance, statistics, Levenberg-Merkert method, Gauss-Newton method, Wolf condition

2023.01.24

アルゴリズム:Algorithms幾何学:Geometry微分積分:Calculus最適化:Optimization機械学習:Machine Learning深層学習:Deep Learning確率・統計:Probability and Statistics線形代数:Linear Algebra

Protected: Unconstrained optimization for continuous optimization in machine learning

Unconstrained Optimization for Continuous Optimization in Machine Learning for Digital Transformation, Artificial Intelligence, and Machine Learning tasks machine epsilon, stopping conditions without scaling, stopping conditions with scaling, Taylor's theorem, stopping conditions for optimization algorithms, Hesse matrix

2022.11.22

アルゴリズム:Algorithms微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra集合論:Set theory

Protected: Fundamentals of Convex Analysis as a Basic Matter for Sequential Optimization in Machine Learning

Basics of convex analysis as a fundamental matter of continuous optimization utilized in digital transformation, artificial intelligence, and machine learning tasks subgradient, subdifferential, conjugate function, closed truly convex function, conjugate function, strongly convex function, closed truly convex function, upper and lower bounds on function values, Hesse matrix, epigraph, Taylor's theorem, relative interior, Ahuynh envelope, continuity, convex envelope, convex function, convex set

2022.11.10

微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra集合論:Set theory

Continuous optimization in machine learning

Sequential optimization, an important computational method for constructing machine learning algorithms used in digital transformation artificial intelligence and machine learning tasks

2022.08.12

アルゴリズム:Algorithmsグラフ理論微分積分:Calculus最適化:Optimization機械学習:Machine Learning確率・統計:Probability and Statistics線形代数:Linear Algebra