Lexicographic Constraint Optimization (LCO)

A Unified Framework for Hierarchical Problem Solving

Author: Antonios Valamontes
Institution: Kapodistrian Academy of Science
License: CC BY-NC 4.0

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What This Repository Is About

This repository contains the full source code, reference implementation, and LaTeX manuscript for the research framework Lexicographic Constraint Optimization (LCO).

LCO is a general-purpose mathematical and computational method for solving problems where objectives must be satisfied in strict priority order, not blended into a single scalar.
Where classical optimization asks "minimize everything at once", LCO asks:

"What must be satisfied first?"

This hierarchical perspective makes certain problems solvable that fail under traditional scalar optimization.

The repository includes working Python code, LaTeX source, and algorithmic templates for applying LCO to mathematics, physics, biology, cognitive modeling, and computational systems.

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Contents of This Repository

This repository is structured into three real components:

1. src/ — Actual Python Code

Contains reference implementations:

• lco.py — The universal LCO solver

  • Takes a list of objective functions [L1, L2, ...]
  • Solves them in strict lexicographic order
  • Returns the highest-tier feasible solution

• algorithms/ — Algorithmic templates

  • Lexicographic descent
  • Tier-by-tier constraint filtering
  • LCO-style search procedures

• examples/ — Example problems

  • Simple mathematical demonstrations
  • Multi-tier constraint systems
  • Educational/clinical tier structures

This is real working code, not pseudocode.

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2. releases/ — Compiled PDF

Contains:

• LCO_Codex_v1.pdf — Final compiled book version
• Future versions will be added with semantic versioning

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How to Use the Python Code

Example:

from lco import LCO

def L1(x): return abs(x - 5)     # Tier 1
def L2(x): return x % 2          # Tier 2
def L3(x): return (x - int(x))**2  # Tier 3

solver = LCO([L1, L2, L3])
solution = solver.solve(0)

print("Solution:", solution)