Thursday, 16 October 2025, 4-5pm Location: 500, 25 Gordon St

• Speaker: Patrick Farrell (Oxford)
  
  Title: The latent variable proximal point algorithm for variational problems with inequality constraints
  
  Abstract:
The latent variable proximal point (LVPP) algorithm is a new framework for solving infinite-dimensional variational problems with inequality constraints. Such problems arise in many applications of mathematics, including in contact and friction, economics, finance, and glaciology, The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretisation. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides. In many cases this mesh independence is achieved for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge-Ampère equation and gracefully handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. In this talk we describe the LVPP algorithm in a general form and apply it to a number of problems from across mathematics.

Thursday, 30 October 2025, 4-5pm Location: 500, 25 Gordon St

Internal Colloquium
Speaker: Mahir Hadzic (UCL)

Title: TBA

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Thursday, 13 November 2025, 4-5pm Location: 500, 25 Gordon St

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Thursday, November 27, 4-5pm Location:500, 25 Gordon St

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Thursday, December 11, 4-5pm Location:500, 25 Gordon St

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You'll find the old colloquium schedules here.