Using Other Solvers

Author

Anqi Fu and Balasubramanian Narasimhan

Introduction

CVXR supports 15 conic and quadratic-program solvers, including several open-source solvers and optional commercial ones, plus two nonlinear-programming (NLP) solvers for disciplined nonlinear programs.

Open Source Solvers (on CRAN)

  • Clarabel, a versatile conic solver written in Rust (default solver).
  • SCS, a conic solver using operator splitting, effective for large-scale problems.
  • OSQP, for quadratic and linear programs.
  • HiGHS, for linear, quadratic, and mixed-integer linear programs.
  • ECOS / ECOS_BB, an interior-point solver for second-order and exponential cone programs (ECOS_BB adds mixed-integer support and is used only when named).
  • GLPK / GLPK_MI, for linear programs and mixed-integer linear programs.
  • CVXOPT, for linear, second-order cone, and semidefinite programs.
  • PIQP, a proximal interior-point solver for quadratic programs.
  • SCIP, for (mixed-integer) LP, QP, and second-order cone programs. Free for academic and non-commercial use; installed from r-universe.

Commercial Solvers

  • MOSEK, supporting LP, QP, SOCP, SDP, exponential/power cone, and mixed-integer programs. Free academic licenses available.
  • Gurobi, supporting LP, QP, SOCP, and mixed-integer programs. Free academic licenses available.
  • CPLEX, supporting LP, QP, SOCP, and mixed-integer programs.
  • FICO Xpress, supporting LP, QP, SOCP, and mixed-integer programs.

Nonlinear (NLP) Solvers

For smooth nonlinear programs — see the DNLP Tutorial, solved with psolve(prob, nlp = TRUE) — CVXR supports two open-source NLP solvers, each via an optional R package in Enhances (not installed by default; CVXR checks for them at solve time and errors informatively if one is missing):

  • Uno (the Uno package), Unifying Nonlinear Optimization. On CRAN and self-contained (bundles its own MUMPS/HiGHS), so it is the practical default for R users; it also recovers dual_value().
  • IPOPT (the ipopt package), an interior-point solver. Not on CRAN owing to licensing, so installed only by determined users; when present, nlp = TRUE prefers it (matching CVXPY).

Solver Capabilities

The table below shows each solver, its R package dependency, and the problem classes it supports.

Solver Capabilities
Solver R Package LP QP SOCP SDP EXP POW MILP MIQP MISOCP
CLARABEL clarabel ✓ ✓ ✓ ✓ ✓ ✓
SCS scs ✓ ✓ ✓ ✓ ✓ ✓
MOSEK* Rmosek ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓ ✓
ECOS ECOSolveR ✓ ✓ ✓ ✓
ECOS_BB ECOSolveR ✓ ✓ ✓ ✓ ✓ ✓ ✓
GUROBI* gurobi ✓ ✓ ✓ ✓ ✓ ✓
GLPK Rglpk ✓
GLPK_MI Rglpk ✓ ✓
HIGHS highs ✓ ✓ ✓
CVXOPT cccp ✓ ✓ ✓ ✓
OSQP osqp ✓ ✓
CPLEX* Rcplex ✓ ✓ ✓ ✓ ✓ ✓
PIQP piqp ✓ ✓
SCIP scip ✓ ✓ ✓ ✓ ✓ ✓
XPRESS* xpress ✓ ✓ ✓ ✓ ✓ ✓

* Commercial solver; free academic licenses are available.

QP: solvers with a quadratic-objective interface receive the objective directly; the other conic solvers solve a second-order-cone reformulation.

Without a commercial solver, mixed-integer problems can use HIGHS or GLPK_MI (MILP only), SCIP (MILP, MIQP, MISOCP) or ECOS_BB.

ECOS_BB is used only when named, as in psolve(prob, solver = "ECOS_BB").

Smooth nonlinear programs, psolve(prob, nlp = TRUE), use the separate NLP solvers Uno or IPOPT; see Using Other Solvers.

Installing Commercial Solvers

MOSEK

MOSEK provides an academic version that is free of charge: one can obtain the free academic license after registering. Once the license for the product has been activated, the Rmosek documentation provides all the details for installation. A quick check to ensure things are working is to run the example:

library(Rmosek)
example(mosek)

Gurobi

Gurobi offers free academic licenses. After installing Gurobi and the gurobi R package (bundled with the Gurobi installation), verify with:

library(gurobi)
model <- list(A = matrix(c(1, 1), nrow = 1),
              obj = c(1, 1), sense = "<=", rhs = 1)
gurobi(model)

CPLEX

IBM CPLEX is available through IBM’s academic initiative. Install the Rcplex package from CRAN after installing the CPLEX library.

Once a commercial solver is installed, you can use it by passing solver = "MOSEK", solver = "GUROBI", or solver = "CPLEX" to psolve().

Session Info

R version 4.6.1 (2026-06-24)
Platform: aarch64-apple-darwin23
Running under: macOS Tahoe 26.6.2

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.6/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

time zone: America/Los_Angeles
tzcode source: internal

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] kableExtra_1.4.1 CVXR_1.9.3      

loaded via a namespace (and not attached):
 [1] Matrix_1.7-6       jsonlite_2.0.0     compiler_4.6.1     highs_1.14.0-2    
 [5] Rcpp_1.1.2         xml2_1.6.0         stringr_1.6.0      dichromat_2.0-1   
 [9] systemfonts_1.3.2  scales_1.4.0       textshaping_1.0.5  yaml_2.3.12       
[13] fastmap_1.2.0      clarabel_0.11.3    here_1.0.2         lattice_0.23-1    
[17] R6_2.6.1           knitr_1.52         htmlwidgets_1.6.4  backports_1.5.1   
[21] tibble_3.3.1       checkmate_2.3.4    rprojroot_2.1.1    osqp_1.0.0        
[25] svglite_2.2.2      pillar_1.11.1      RColorBrewer_1.1-3 rlang_1.3.0       
[29] stringi_1.8.9      xfun_0.61          S7_0.2.2           otel_0.2.0        
[33] viridisLite_0.4.3  cli_3.6.6          magrittr_2.0.5     digest_0.6.39     
[37] grid_4.6.1         rstudioapi_0.19.0  gmp_0.7-5.1        lifecycle_1.0.5   
[41] vctrs_0.7.3        scs_3.2.7          evaluate_1.0.5     glue_1.8.1        
[45] farver_2.1.2       rmarkdown_2.32     pkgconfig_2.0.3    tools_4.6.1       
[49] htmltools_0.5.9

References