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DSOS and SDSOS optimization: more tractable alternatives to sum of squares and semidefinite optimization
In recent years, optimization theory has been greatly impacted by the advent of sum of
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …
squares (SOS) optimization. The reliance of this technique on large-scale semidefinite …
[HTML][HTML] (Global) optimization: historical notes and recent developments
Abstract Recent developments in (Global) Optimization are surveyed in this paper. We
collected and commented quite a large number of recent references which, in our opinion …
collected and commented quite a large number of recent references which, in our opinion …
Clarabel: An interior-point solver for conic programs with quadratic objectives
We present a general-purpose interior-point solver for convex optimization problems with
conic constraints. Our method is based on a homogeneous embedding method originally …
conic constraints. Our method is based on a homogeneous embedding method originally …
[HTML][HTML] Shape-constrained multi-objective genetic programming for symbolic regression
We describe and analyze algorithms for shape-constrained symbolic regression, which
allow the inclusion of prior knowledge about the shape of the regression function. This is …
allow the inclusion of prior knowledge about the shape of the regression function. This is …
Solving natural conic formulations with Hypatia. jl
Many convex optimization problems can be represented through conic extended
formulations (EFs) using only the small number of standard cones recognized by advanced …
formulations (EFs) using only the small number of standard cones recognized by advanced …
Bounds on mean energy in the Kuramoto–Sivashinsky equation computed using semidefinite programming
We present methods for bounding infinite-time averages in dynamical systems governed by
nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov …
nonlinear PDEs. The methods rely on auxiliary functionals, which are similar to Lyapunov …
alfonso: Matlab package for nonsymmetric conic optimization
We present alfonso, an open-source Matlab package for solving conic optimization
problems over nonsymmetric convex cones. The implementation is based on the authors' …
problems over nonsymmetric convex cones. The implementation is based on the authors' …
Bounding extreme events in nonlinear dynamics using convex optimization
We study a convex optimization framework for bounding extreme events in nonlinear
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …
dynamical systems governed by ordinary or partial differential equations (ODEs or PDEs) …
Performance enhancements for a generic conic interior point algorithm
In recent work, we provide computational arguments for expanding the class of proper cones
recognized by conic optimization solvers, to permit simpler, smaller, more natural conic …
recognized by conic optimization solvers, to permit simpler, smaller, more natural conic …
Koopman-based neural Lyapunov functions for general attractors
Koopman spectral theory has grown in the past decade as a powerful tool for dynamical
systems analysis and control. In this paper, we show how recent data-driven techniques for …
systems analysis and control. In this paper, we show how recent data-driven techniques for …