(Senior) Optimization Engineer

We’re on a mission to do something really, really small. You’ll craft the masks that bring our patterns to life. Lace Lithography is seeking a highly experienced Senior Optimization Engineer to join our Mask Design team. In this high-impact role, you will architect and deploy the advanced nonlinear optimization engines that define the theoretical limits of our lithography systems. You will be responsible for defining how we solve high-dimensional, nonlinear problems, mentoring the team on advanced numerical methods, and establishing the standards for optimization reliability. Working alongside physicists and developers, you will deliver high-performance solutions to critical manufacturing challenges. This role is based in Barcelona, and will involve regular travel between our two locations throughout the year. What you’ll do Advanced Algorithm Engineering: Design and engineer custom, large-scale nonlinear optimization algorithms. You will move beyond standard implementations to develop specialized heuristics and globalization strategies that exploit the specific structure of our problem. Complex Mathematical Formulation: Translate intricate multiphysics phenomena into rigorous, differentiable optimization problems, ensuring well-posedness and numerical stability for complex engineering objectives. Deep Solver Integration & Customization: Go beyond basic API interfacing to deeply customize solver behaviors. You will modify linear algebra backends, Hessian approximations, and callback structures to maximize solver performance. Code Implementation: Write highly optimized, modular, and testable scientific code in Julia, Python, or C++. GPU-Accelerated Optimization: Implement distributed and GPU-accelerated optimization routines. You will apply parallelization strategies (MPI, CUDA/Kernel abstractions) required to solve problems with millions of degrees of freedom in viable timeframes. Algorithmic Tuning & Profiling: Conduct deep‑dive performance analysis on critical loops. You will profile memory access patterns and algorithmic complexity to eliminate bottlenecks and resolve numerical instabilities. Testing and Validation: Design comprehensive validation frameworks that stress‑test optimization convergence and ensure robustness against real‑world edge cases. Cross‑Disciplinary Collaboration: Work closely with physics and hardware teams to ensure strong alignment between mathematical models and real‑world systems. Technical Standards & Best Practices: Serve as a Subject Matter Expert (SME) on numerical optimization. You will elevate the team's technical bar by conducting rigorous code reviews and championing best practices in numerical computing. Who you are Required: Education & Experience: PhD in Applied Mathematics, Computer Science, Computational Physics, or Operations Research (or a Master’s degree with extensive industrial experience in numerical computing). Expert Optimization Theory: Deep command of nonlinear optimization theory, including KKT conditions, duality, and the mechanics of Interior Point or Trust-Region methods. Large‑Scale Solving: Proven track record of formulating and solving massive‑scale optimization problems (1M+ variables) in production or high-performance research contexts. Scientific Coding Mastery: Advanced proficiency in Julia, C++, or Python, with a strong focus on type stability, memory allocation, and vectorization. Numerical Linear Algebra: Deep knowledge of sparse matrix factorizations, iterative linear solvers, and preconditioning techniques. Solver Expertise: Hands‑on experience tuning and interfacing with large-scale solvers (e.g., IPOPT, KNITRO, SNOPT) at a low level. Debugging & Stability: Ability to diagnose complex convergence failures (singularities, scaling issues) and re‑formulate problems for numerical stability. Software Engineering Rigor: Strong discipline in modern software practices, including version control (Git), unit testing for numerical code, and CI/CD workflows. Technical Communication: Ability to distill complex mathematical trade‑offs into clear engineering decisions. Preferred: Exposure to GPU programming, high-performance computing, or parallel algorithms Experience contributing to scientific software projects or open-source tools Our team here at Lace …consists of amazing people who’ve joined us from all over the world, driven by intense curiosity, the urge for exploration, and a desire to push the limits of physics. We promise to offer you a place among highly motivated Lacers, present you with extremely difficult problems - and have a lot of fun solving them. Workplace & culture Lace operates out of two beautiful, vibrant, and strong‑willed cities. Although we are cities apart, we strive to make the team feel as one. We don’t define values - but we have one universal expectation:Be the best team player you can be. Perks and Benefits