---
name: convex-optimization-solver
description: Solve convex optimization problems efficiently
allowed-tools:
  - Bash
  - Read
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metadata:
  specialization: mathematics
  domain: science
  category: optimization
  phase: 6
---

# Convex Optimization Solver

## Purpose

Provides capabilities for formulating and solving convex optimization problems efficiently and reliably.

## Capabilities

- Linear programming (LP)
- Quadratic programming (QP)
- Second-order cone programming (SOCP)
- Semidefinite programming (SDP)
- Conic optimization
- Duality analysis

## Usage Guidelines

1. **Convexity Verification**: Confirm problem convexity
2. **Formulation**: Express problem in standard conic form
3. **Solver Selection**: Choose solver based on problem structure
4. **Duality**: Extract dual variables for sensitivity analysis

## Tools/Libraries

- CVXPY
- Gurobi
- MOSEK
- SCS
- ECOS