Optimality Conditions

Protected: Optimization for the main problem in machine learning

Optimization for main problems in machine learning used in digital transformation, artificial intelligence, and machine learning tasks (barrier function method, penalty function method, globally optimal solution, eigenvalues of Hesse matrix, feasible region, unconstrained optimization problem, linear search, Lagrange multipliers for optimality conditions, integration points, effective constraint method)

2023.05.02

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: Optimality conditions for constrained inequality optimization problems in machine learning

Optimality conditions for constrained inequality optimization problems in machine learning used in digital transformation, artificial intelligence, and machine learningtasks duality problems, strong duality, Lagrangian functions, linear programming problems, Slater conditions, principal dual interior point method, weak duality, first order sufficient conditions for convex optimization, second order sufficient conditions, KKT conditions, stopping conditions, first order optimality conditions, valid constraint expressions, Karush-Kuhn-Tucker, local optimal solutions

2023.04.19

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: Optimality conditions for equality-constrained optimization problems in machine learning

Optimality conditions for equality-constrained optimization problems in machine learning utilized in digital transformation, artificial intelligence, and machine learning tasks (inequality constrained optimization problems, effective constraint method, Lagrange multipliers, first order independence, local optimal solutions, true convex functions, strong duality theorem, minimax theorem, strong duality, global optimal solutions, second order optimality conditions, Lagrange undetermined multiplier method, gradient vector, first order optimization problems)

2023.04.05

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 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: Optimality conditions and algorithm stopping conditions in machine learning

Optimality conditions and algorithm stopping conditions in machine learning used in digital transformation, artificial intelligence, and machine learning scaling, influence, machine epsilon, algorithm stopping conditions, iterative methods, convex optimal solutions, constrained optimization problems, global optimal solutions, local optimal solutions, convex functions, second order sufficient conditions, second order necessary conditions, first order necessary conditions

2022.12.06

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