Article-22714-SLSQP-MQL5-Volatility-Library-Integration

Overview

This reference project is based on an MQL5 article describing a native Sequential Least Squares Programming (SLSQP) optimizer for constrained nonlinear optimization and its integration into an existing conditional volatility library intended to mirror Python's arch module behavior.

The article focuses on:

• diagnosing parameter discrepancies between MetaTrader 5 and Python volatility models,
• replacing ALGLIB minNLC with SLSQP,
• exposing an object-oriented MQL5 interface for objective functions and constraints,
• and validating improved cross-platform agreement on ARCH/GARCH-family models.

Original Article

• Article ID: 22714
• Author: Francis Dube
• Publication date: 2026.05.30
• Category: Articles / MQL5 programming / optimization / quantitative finance
• URL: https://www.mql5.com/en/articles/22714

Repository Purpose

This repository should be understood as a reference/reconstruction project for the article’s code and architecture.

Its purpose is to preserve the implementation concepts presented in the article:

• an MQL5 port of the original Fortran SLSQP algorithm,
• a CSlsqp solver interface,
• constraint wrappers via CConstraints,
• objective wrappers via CFunctor,
• optional numerical or analytical gradients,
• and conditional integration into a volatility modeling library through the __SLSQP__ macro.

Key Concepts

• Sequential Least Squares Programming (SLSQP)
• constrained nonlinear optimization
• KKT conditions
• active-set constraint handling
• equality and inequality constraints
• finite-difference numerical differentiation
• analytical Jacobians/gradients
• conditional volatility models
• cross-platform parity with Python arch
• conditional compilation for optimizer selection

Algorithm / Architecture Summary

The article describes an MQL5-native SLSQP implementation centered around slsqp.mqh, with an object-oriented class CSlsqp used to configure and execute optimization.

Key architectural elements mentioned in the article:

• Objective interface

• objective functions derive from CFunctor

• core function implemented through orig_fun()

• optional analytical gradient via grad_fun()

• Constraint interface

• constraints derive from CConstraints

• equality constraints use the form h(x)=0

• inequality constraints use the form g(x)<=0

• optional analytical Jacobian through orig_grad()

• Differentiation support

• numerical differentiation utilities are supplied through num_diff.mqh

• ObjReturn is extended to support scalar/vector outputs and gradient/Jacobian data

• Solver configuration

• bounds, tolerances, stopping conditions, maximum evaluations, and target stop values

• methods include SetEqualityConstraints(), SetInequalityConstraints(), SetXtolRel(), SetFtolRel(), SetFtolAbs(), SetXtolAbs(), SetMaxEval(), SetStopVal(), and SetAcc()

• Execution result

• optimization returns an OptimizeResult structure containing return code, function evaluations, iterations, solution, objective value, and gradient

• Volatility library integration

• the article shows conditional inclusion of slsqp.mqh in mean.mqh

• under __SLSQP__, HARX fitting uses SLSQP-based wrappers for objective and inequality constraints

• without the macro, the legacy ALGLIB path remains active

The article’s validation section reports that after integration, MQL5 model parameters and log-likelihood values become closely aligned with Python arch results for several ARCH/GARCH-family specifications.

Tags

MQL5, SLSQP, Optimization, Constrained-Optimization, ARCH, GARCH, Volatility-Modeling, Python-ARCH, Numerical-Differentiation, Quantitative-Finance

Difficulty

Advanced

Requires familiarity with:

• nonlinear constrained optimization,
• gradients and Jacobians,
• KKT conditions,
• MQL5 OOP patterns,
• and volatility model fitting workflows.

Reference

Original MQL5 article: https://www.mql5.com/en/articles/22714