Initialize optimization problems repository with structure and examples

[Copilot]

Creates a crowdsourced repository for tracking mathematical optimization problems and their optimal constants with known bounds.

Structure

• README.md: Index of problems organized by domain (Analysis, Discrete Mathematics)
• template.md: Standardized format for problem documentation
• problems/: Individual problem files with bounds, references, and history
• CONTRIBUTING.md: Guidelines for adding problems and updating bounds

Example Problems

Three problems demonstrate the template format:

1. Sobolev Inequality (Analysis): Sharp constants for W^{1,p}(ℝ^n) → L^{p*}(ℝ^n) embedding
2. Hardy Inequality (Analysis): Optimal constants for 1D and n-dimensional cases
3. Erdős-Ko-Rado (Discrete): Maximum size of intersecting k-subset families

Each problem includes:

• Precise problem statement with mathematical notation
• Current best upper/lower bounds with citations
• Historical timeline of improvements
• Complete references to literature

Format

Problems follow a consistent structure:

## Current Best Bounds

### Upper Bound
- **Value**: [expression]
- **Reference**: Author(s), Year, Journal
- **Note**: [method or significance]

### Lower Bound
- **Value**: [expression]  
- **Reference**: Author(s), Year, Journal

Contributors can submit PRs to add new problems or update bounds with proper citations.

Original prompt

I would like to create a repository of optimization problems in mathematics - problems where there is some constant C arising from an optimization problem - for instance the best constant for which a certain inequality is true - and record the known upper/lower bounds, with the aim to encourage crowdsourced updating of these records with pull requests. I'm thinking to start with a simple interface to begin with: a README with a list of links to other Markdown files, one for each problem.

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