---
title: "SOLNP Test Suite"
output: 
    rmarkdown::html_vignette:
        css: custom.css
        code_folding: hide
        citation_package: natbib
        toc: yes
bibliography: references.bib
bibliography-style: apalike
natbiboptions: round
vignette: >
  %\VignetteIndexEntry{SOLNP Test Suite}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

```{r setup, echo=FALSE}
library(Rsolnp)
```

## Introduction


The purpose of the new SOLNP Test Suite is to provide a comprehensive, 
standardized environment for benchmarking and validating nonlinear optimization 
algorithms, with a particular focus on the SOLNP family of solvers. The suite is 
anchored around the well-known Hock-Schittkowski (HS) test problems, a diverse 
collection of nonlinear programming challenges that have become a benchmark 
standard in the optimization literature.

This suite currently implements 64 of the HS problems, spanning a range of 
complexities, constraint types, and objective function characteristics. Future 
updates will expand coverage to include the entire set of 306 Hock-Schittkowski 
problems, ensuring a thorough and robust testing ground for both algorithmic 
development and comparative analysis.

The problems are currently stored in a form compatible with the SOLNP solver, 
enabling immediate use for benchmarking and analysis. However, recognizing that 
nonlinear programming (NLP) problems can be specified in various formats—sometimes 
with differing conventions for constraints, bounds, and objective function 
representation—the suite includes a utility function called `solnp_standardize_problem`
which rewrites the test in the NLP standard form (e.g. as used by [nloptr](https://CRAN.R-project.org/package=nloptr)).

A distinctive feature of several HS problems is that their optimal solutions 
often occur on or very near the boundary of the feasible region, where one or more 
inequality constraints are active. In other words, the optimal solution frequently 
coincides with points where the constraints are "tight", and further movement 
would violate feasibility.

This aspect is of particular importance for algorithm development, as it tests 
a solver's ability to:

  * Correctly identify the active set of constraints at the optimum,
  * Handle boundary solutions robustly, and
  * Maintain numerical stability and feasibility in the presence of active inequality constraints.

It should be noted that SOLNP does not employ an active set strategy. Instead, 
its augmented Lagrangian approach treats constraints via penalty terms, and the 
optimizer does not explicitly identify or maintain sets of active constraints 
during the iterations. As a result, SOLNP solutions typically remain in the 
interior of the feasible region whenever possible, only approaching the boundary 
when required for optimality.



## Usage

The function `solnp_problems_table` lists the problem currently implemented:

```{r}
head(solnp_problems_table())
```


whilst the function `solnp_problem_suite` can either return a specific problem
or all problems within a Suite:

```{r}
prob <- solnp_problem_suite(suite = "Hock-Schittkowski", number = 60)
sol <- csolnp(prob$start, fn = prob$fn, gr = prob$gr, eq_fn = prob$eq_fn, 
              eq_b = prob$eq_b, eq_jac = prob$eq_jac, ineq_fn = prob$ineq_fn, 
              ineq_lower = prob$ineq_lower, ineq_upper = prob$ineq_upper, 
              ineq_jac = prob$ineq_jac, lower = prob$lower, upper = prob$upper, 
              control = list(trace = 0, min_iter = 1000, max_iter = 300, tol = 1e-8, rho = 1))
print(c("solnp" = sol$objective, "benchmark" = prob$best_fn))
print(rbind("solnp" = sol$pars, "benchmark" = prob$best_par))
```