Sparse SDP support

[angeloskorakitis]

Benchmark: Sparse SDP Problems

Test configuration

Parameters used for simulated annealing

• CONSTANT_1 20
• walkLength = 3
• convergenceWindow_ = 9
• (the rest remained the same)

Important Note: For Volesti these benchmarks use the origin as the initial point without explicitly computing an interior point.

Results

Library	Instance	Expected Min	Computed Min	Error	Status	Time
Volesti	Sparse 30x100	-1.0494e+01	-1.0442e+01	5.22e-02	✅ PASS	0.372s
SDPA	Sparse 30x100	-1.0494e+01	-1.9713e+01	9.22e+00	❌ FAIL*	0.558s
Volesti	Sparse 40x100	-1.4262e+01	-1.4023e+01	2.39e-01	✅ PASS	0.651s
SDPA	Sparse 40x100	-1.4262e+01	-5.5061e+00	8.76e+00	❌ FAIL*	0.868s
Volesti	Sparse 40x300	-4.3696e+00	-4.3213e+00	4.83e-02	✅ PASS	4.876s
SDPA	Sparse 40x300	-4.3696e+00	-2.6647e+00	1.70e+00	❌ FAIL*	5.839s
Volesti	Sparse 50x200	-9.5851e+00	-9.2579e+00	3.27e-01	✅ PASS	1.624s
SDPA	Sparse 50x200	-9.5851e+00	+7.3211e+00	1.69e+01	❌ FAIL*	1.838s

*SDPA failures are due to large primal feasibility errors (>100), indicating the solver did not converge to a feasible solution on these sparse instances.

Key Observations

• Sparse Problem Handling: Volesti successfully solves all sparse SDP instances, while SDPA fails on all sparse test cases
• Performance: Volesti maintains competitive speed even on sparse problems (40x300 with 951k sparse entries solved in ~5s)
• Accuracy: Volesti achieves good approximations

Sparse Problem Details

Instance	Sparse Entries	Sparsity Pattern
30x100	81,550	~9.05% density
40x100	107,050	~6.69% density
40x300	951,150	~19.81% density
50x200	525,100	~10.50% density