Stochastic Gradient Descent: Optimization and Convergence Analysis

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Explores stochastic gradient descent, covering convergence rates, acceleration, and practical applications in optimization problems.

Explores iterative methods for solving nonlinear equations, discussing convergence properties and implementation details.

Explores the convergence analysis of Newton's method for solving nonlinear equations, discussing linear and quadratic convergence properties.

Explores optimization in energy system modeling, covering decision variables, objective functions, and different strategies with their pros and cons.

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Covers generalized integrals, convergence criteria, series convergence, and harmonic series in analysis.

Covers the proof of the Squeeze Theorem, Quotient Criteria, and the Bolzano-Weierstrass Theorem.

Explores the convergence and limit of geometric series, demonstrating mathematical properties and applications.