Indigenous GPU-Accelerated Optimization Solver.
First-order Primal-Dual Hybrid Gradient (PDHG) algorithms and Branch-and-Bound search for massive-scale LP, QP, and MILP industrial workloads.
The Industrial Decision Problem
Industrial operations cannot optimize isolated variables. Altering a single blending quota or unit schedule triggers cascading constraint violations across power, inventory, and transportation.
Directly determines crude throughput and refinery capacity utilization.
How the Solver Operates
Click any step to inspect the underlying mathematical formulation, CUDA execution model, and asymptotic complexity.
Decision Vector Space
High-dimensional parameter space where decision vectors x ∈ ℝⁿ are mapped across objective cost gradients ∇f(x).
Constrained Polytope
Constraint hyperplanes intersect to carve out an enclosed convex polytope containing all physically admissible decisions.
Primal-Dual Operator Step
First-order operator splitting navigates high dimensions via GPU-accelerated sparse matrix-vector products.
KKT Certified Optimum
Rigorous duality gap computation verifies zero constraint violation and certifies global mathematical optimality.
Architectural Control
A technical comparison of standard proprietary dependencies versus our indigenous stack.
Dependency Stack
Indigenous Stack
Control
Full ownership of the mathematical execution path and optimization parameters.
Transparency
Inspect exactly how constraints are processed and variables bounded.
Extensibility
Modify numerical kernels directly to support specialized problem structures.
Execution Pipeline
The solver maps high-level mathematical structures down to hardware-optimized numerical operations. Each stage is designed for maximum throughput.
View full architecture detailsReads MPS format problem files and constructs sparse matrix structures.
Solver Capabilities
A versatile mathematical engine designed for the complexities of modern industrial problems.
Continuous Optimization
Our core engine utilizes the Primal-Dual Hybrid Gradient (PDHG) method for Linear Programming (LP). This first-order approach avoids the costly matrix factorizations required by traditional Interior Point Methods, enabling it to scale efficiently to massive, highly sparse industrial instances. Quadratic Programming (QP) is fully supported for problems requiring non-linear objectives.
Discrete Optimization
For discrete decisions—such as scheduling, equipment activation, or step-function costs—the solver includes a custom Branch-and-Bound (B&B) framework. It recursively partitions the Mixed-Integer Linear Programming (MILP) search space, utilizing the continuous LP solver to evaluate node relaxations and efficiently prune suboptimal branches.
Heterogeneous Computing
GPU acceleration is used selectively for operations that benefit from massive parallelism, coordinated closely with the CPU.
Orchestration
- ▪Model management and parsing
- ▪Presolve and problem reduction
- ▪Branch-and-bound tree control
- ▪Heuristics and solver state orchestration
Acceleration
- ▪Sparse matrix-vector multiplications (SpMV)
- ▪Highly parallel numerical kernels
- ▪Vector additions and dot products
- ▪Massive throughput for PDHG iterations
Performance Benchmarks
No benchmark data yet — Run a benchmark to populate results.
| Instance | Class | Variables | Constraints | Runtime | Status |
|---|---|---|---|---|---|
| production_planning_v2.mps | LP | 125,000 | 84,500 | -- | Pending |
| logistics_network_eu.mps | MILP | 42,000 | 51,200 | -- | Pending |
| portfolio_risk_model.mps | QP | 15,000 | 12,000 | -- | Pending |
Ready to deploy the solver?
Run industrial LP/QP/MILP benchmarks, test custom MPS files, and inspect KKT convergence directly in your browser.