Update documentation with details of HiPO

Author: filikat

docs/src/options/definitions.md

@@ -6,7 +6,7 @@
 - Default: "choose"
 
 ## [solver](@id option-solver)
-- Solver option: "simplex", "choose", "ipm" or "pdlp". If "simplex"/"ipm"/"pdlp" is chosen then, for a MIP (QP) the integrality constraint (quadratic term) will be ignored
+- Solver option: "simplex", "choose", "ipm", "hipo" or "pdlp". If "simplex"/"ipm"/"hipo"/"pdlp" is chosen then, for a MIP (QP) the integrality constraint (quadratic term) will be ignored
 - Type: string
 - Default: "choose"
 
@@ -414,6 +414,22 @@
 - Range: {0, 2147483647}
 - Default: 2147483647
 
+## [hipo\_system](@id option-hipo-system)
+- Type of Newton system for HiPO: "augmented", "normaleq" or "choose"
+- Type: string
+- Default: "choose"
+
+## [hipo\_parallel\_type](@id option-hipo-parallel)
+- Type of parallelism for HiPO: "tree", "node", "both"
+- Type: string
+- Default: "both"
+
+## hipo\_block\_size
+- Block size for dense linear algebra within HiPO
+- Type: integer
+- Range: {0, 2147483647}
+- Default: 128
+
 ## pdlp\_native\_termination
 - Use native termination for PDLP solver: Default = false
 - Type: boolean

docs/src/parallel.md

@@ -4,10 +4,10 @@
 
 HiGHS currently has limited opportunities for exploiting parallel
 computing. When using a CPU, these are currently restricted to the
-dual simplex solver for LP, and the MIP solver. Details of these and
-future plans are set out below. HiGHS has an implementation of a first
-order method (PDLP) for solving LPs that can exploit the availability of a
-[GPU](@ref highs-gpu).
+dual simplex solver for LP, the factorisation-based interior point solver,
+and the MIP solver. Details of these and future plans are set out below. 
+HiGHS has an implementation of a first order method (PDLP) for solving LPs 
+that can exploit the availability of a [GPU](@ref highs-gpu).
 
 By default, when running in parallel, HiGHS will use half the
 available threads on a machine. This number can be modified by setting
@@ -47,14 +47,32 @@ clique tables, and when the interior point solver is used to compute
 the analytic centre. This parallelism is always advantageous, so is
 performed regardless of the value of the [parallel](@ref) option.
 
+## IPM
+
+The interior point solver HiPO uses multiple threads to process the 
+elimination tree during the multifrontal factorisation (_tree level_)
+and to perform the dense factorisation of the frontal matrices 
+(_node level_).
+
+If the [parallel](@ref) option is set "on", the level of parallelism is 
+determined by the [hipo\_parallel\_type](@ref option-hipo-parallel) option, 
+which can be "tree" for tree level only, "node" for node level only, or 
+"both" for both levels.
+
+If the [parallel](@ref) option is set "choose", the solver selects which 
+level to use based on a heuristic. When the [parallel](@ref) option is set 
+"choose" or "off", the value of the hipo\_parallel\_type option is ignored.
+
+
 ## Future plans
 
 The MIP solver has been written with parallel tree search in mind. Some
 work has started (Feb 2025), and it is hoped that a prototype solver
 will be available during 2025.
 
-Development of a new parallel interior point solver began 2023, and a
-prototype solver is expected to be be available during 2025.
+Multi-threading within HiPO will be extended to other phases of the solver,
+including the solve phase of the factorisation and the process of assemblying 
+the matrices.
 
 First-order solvers for LP are still very much in their infancy, and
 are not robust. Hence the availability of a PDLP solver for LP is

docs/src/solvers.md

@@ -26,15 +26,30 @@ J. A. J. Hall, Mathematical Programming Computation, 10 (1), 119-142,
 
 #### Interior point
 
-HiGHS has one interior point (IPM) solver based on the preconditioned conjugate gradient method, as discussed in
+HiGHS has two interior point (IPM) solvers:
 
-_Implementation of an interior point method with basis
-preconditioning_, Mathematical Programming Computation, 12, 603-635, 2020. [DOI:
-10.1007/s12532-020-00181-8](https://link.springer.com/article/10.1007/s12532-020-00181-8).
+* IPX is based on the preconditioned conjugate gradient method, as discussed in
 
-This solver is serial. An interior point solver based on direct factorization is being developed.
+  _Implementation of an interior point method with basis
+  preconditioning_, Mathematical Programming Computation, 12, 603-635, 2020. [DOI:
+  10.1007/s12532-020-00181-8](https://link.springer.com/article/10.1007/s12532-020-00181-8).
 
-Setting the option [__solver__](@ref option-solver) to "ipm" forces the IPM solver to be used
+  This solver is serial.
+
+  Setting the option [__solver__](@ref option-solver) to "ipm" forces the IPX solver to be used
+
+* HiPO is based on a direct factorisation, as discussed in 
+
+  _A factorisation-based regularised interior point method using the augmented system_, F. Zanetti and J. Gondzio, 2025, 
+  [available on arxiv](https://arxiv.org/abs/2508.04370)
+
+  This solver is parallel.
+
+  Setting the option [__solver__](@ref option-solver) to "hipo" forces the HiPO solver to be used.
+
+  The [hipo\_system](@ref option-hipo-system) option can be used to select the approach to use when solving the Newton systems 
+  within the interior point solver: select "augmented" to force the solver to use the augmented system, "normaleq" for normal 
+  equations, or "choose" to leave the choice to the solver.
 
 #### Primal-dual hybrid gradient method
 
@@ -53,7 +68,7 @@ The HiGHS MIP solver uses established branch-and-cut techniques
 ## QP
 
 The HiGHS solver for convex QP problems uses an established primal
-active set method. The new interior point solver will also be able to
+active set method. The new interior point solver HiPO will soon be able to
 solve convex QP problems.