Okay, I need to write a professional wiki-style document in Korean about "Non-convex Optimization" under the categories of Technology, Data Science, and Analysis. Let me start by understanding what the user is asking for.

, the structure. The document should have an H1 title, an overview/introduction section, several detailed sections using H2 and H3, and possibly a references or related documents section. The content needs to be accurate, objective, with appropriate depth and easy to understand. Also, use markdown formatting properly, including lists, tables, code blocks if needed.

The title is given as "비볼록 최적화" (Non-convex Optimization). The main categories are Technology → Data Science → Analysis. So the document should focus on non-convex optimization in the context of data science.

Starting with the overview. I should explain what non-convex optimization is, contrasting it with convex optimization. Mention that convex problems have a single global minimum, while non-convex can have multiple local minima and saddle points. Highlight the importance in data science, especially in machine learning models like neural networks.

Next, detailed sections. Let me think about possible H2 sections. Maybe:

1. 비볼록 최적화의 정의 및 개념
2. 주요 도전 과제
3. 주요 알고리즘 및 기법
4. 응용 분야
5. 최근 연구 동향
6. 참고 자료 및 관련 문서

Under each H2, I can break into H3s. For example, under 주요 알고리즘, I can list Gradient Descent, Stochastic Gradient Descent, Momentum, Adam, 그리고 글로벌 최적화 기법 like Simulated Annealing, Genetic Algorithms.

For 도전 과제, discuss local minima, saddle points, computational complexity, convergence issues.

In 응용 분야, mention deep learning, recommendation systems, computer vision, NLP.

Need to ensure technical terms are explained simply. For instance, explain what a saddle point is in the context of optimization.

Also, include examples or simple code blocks if applicable. Maybe a code example using PyTorch for optimization? Though since it's a general document, maybe not necessary unless the user specifies. The original example didn't have code, so maybe just describe algorithms without code.

Make sure to mention recent trends like the use of second-order methods, adaptive algorithms, and metaheuristics.

References should include key papers, books, or online resources. Maybe cite Boyd and Vandenberghe for convex optimization, papers on Adam optimizer, and recent surveys on non-convex optimization in machine learning.

Check for length: need at least 800 characters. Since the sample response is in Korean and detailed, I need to ensure each section is sufficiently expanded.

Let me start drafting each section.

For the introduction: Define non-convex optimization, explain why it's important in data science. Mention that many real-world problems are non-convex.

In the definition section, compare convex vs. non-convex functions. Use mathematical terms but explain them. For example, convex function: f(λx + (1-λ)y) ≤ λf(x) + (1-λ)f(y). For non-convex, this doesn't hold.

Challenges: Local minima vs. global, saddle points, which are common in high dimensions. Computational issues due to complex landscapes.

Algorithms: Gradient descent, SGD, Momentum, Adam. Explain each briefly. Then global methods like simulated annealing, genetic algorithms, particle swarm optimization. Maybe mention stochastic tunneling.

Applications: Deep learning models (CNNs, RNNs), training large models with non-convex loss surfaces. Recommender systems with matrix factorization, which is non-convex.

Recent trends: Use of adaptive learning rates, combination of first and second-order methods, research on saddle point escape, and better initialization techniques.

References: Include books, key papers (like Kingma's Adam), recent articles, and links to relevant courses or surveys.

Need to ensure the document flows logically, each section connects, and information is accurate. Also, check for any technical inaccuracies. For example, simulated annealing is a probabilistic technique, genetic algorithms use evolutionary approaches.

Avoid overly complex jargon without explanation. Keep paragraphs concise for readability.

I think that's a solid outline. Now, structure the markdown accordingly, using H1, H2, H3 headings, bullet points where needed, and tables if helpful. Since it's a Korean document, make sure all terms are appropriately translated or noted with English terms in parentheses.

Double-check the length by ensuring each section has enough content. For example, each H2 section should have a few paragraphs or bullet points. The sample response provided by the user is quite detailed, so follow that style.