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This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
While automatically generated polynomial elimination templates have sparked great progress in the field of 3D computer vision, there remain many problems for which the degree of the constraints or the number of unknowns leads to…
We develop a computationally efficient algorithm for the automatic regularization of nonlinear inverse problems based on the discrepancy principle. We formulate the problem as an equality constrained optimization problem, where the…
In this paper, we consider a Model Predictive Control (MPC) problem of a continuous-time linear time-invariant system subject to continuous-time path constraints on the states and the inputs. By leveraging the concept of differential…
Recent advancements in data science have significantly elevated the importance of orthogonally constrained optimization problems. The Riemannian approach has become a popular technique for addressing these problems due to the advantageous…
We propose a class of multipliers correction methods to minimize a differentiable function over the Stiefel manifold. The proposed methods combine a function value reduction step with a proximal correction step. The former one searches…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
Recent studies have shown that proximal gradient (PG) method and accelerated gradient method (APG) with restarting can enjoy a linear convergence under a weaker condition than strong convexity, namely a quadratic growth condition (QGC).…
In this manuscript, we propose a general proximal quasi-Newton method tailored for nonconvex and nonsmooth optimization problems, where we do not require the sequence of the variable metric (or Hessian approximation) to be uniformly bounded…
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…
We introduce an innovative numerical technique based on convex optimization to solve a range of infinite dimensional variational problems arising from the application of the background method to fluid flows. In contrast to most existing…
Homotopy methods are attractive due to their capability of solving difficult optimisation and optimal control problems. The underlying idea is to construct a homotopy, which may be considered as a continuous (zero) curve between the…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
This paper presents an efficient gradient projection-based method for structural topological optimization problems characterized by a nonlinear objective function which is minimized over a feasible region defined by bilateral bounds and a…
In this paper, we consider the minimization of a nonsmooth nonconvex objective function $f(x)$ over a closed convex subset $\mathcal{X}$ of $\mathbb{R}^n$, with additional nonsmooth nonconvex constraints $c(x) = 0$. We develop a unified…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
In this work, we propose a high-order multiscale method for an elliptic model problem with rough and possibly highly oscillatory coefficients. Convergence rates of higher order are obtained using the regularity of the right-hand side only.…
A sequential quadratic optimization algorithm is proposed for solving smooth nonlinear equality constrained optimization problems in which the objective function is defined by an expectation of a stochastic function. The algorithmic…
We propose smoothed primal-dual algorithms for solving stochastic and smooth nonconvex optimization problems with linear inequality constraints. Our algorithms are single-loop and only require a single stochastic gradient based on one…