2025-07-23 –, Main Room 6
Mathematical optimization is ubiquitous in scientific and engineering domains. We will explore how ConicSolve.jl, a Julia package is utilized to solve a variety of problem classes, including Linear (LP), Quadratic (QP), Second Order Cone (SOCP), and Semidefinite Programming (SDP). We'll cover examples in robotics, imaging and comms to discuss the techniques in modelling optimization problems and the design decisions made to make ConicSolve.jl a performant, versatile and extensible framework.
Mathematical optimization is used in many scientific and engineering domains, from robotics and image processing to communications. In robotics, for example, optimization helps compute collision-free trajectories; in image processing (e.g., MRI or Magnetic Resonance Imaging), it aids in denoising through matrix completion; and in network design, it enables maximizing data throughput subject to capacity constraints (e.g., Max Flow Min Cut).
This talk focuses on constrained optimization problems and how Interior-point Methods (IPMs) are applied to efficiently solve them. We will explore how ConicSolve.jl, a Julia package, implements these methods to handle a variety of problem classes, including Linear Programming (LP), Quadratic Programming (QP), Second Order Cone Programming (SOCP), and Semidefinite Programming (SDP).
We will discuss key challenges in solving large-scale constrained optimization problems, especially when dealing with thousands of constraints and explain how array manipulation techniques and thoughtful API design decisions in ConicSolve.jl simplify the process for practitioners.
Additionally, we'll explore strategies such as exploiting problem structure and sparsity to enhance solver performance. This talk will include practical examples, such as image denoising and max flow min cut, to demonstrate the utility of solvers based on Conic IPMs.
By the end of the session, you'll have a deeper understanding of the optimization modeling process and a set of tools to tackle the common challenges faced when solving constrained optimization problems.
