Related papers: Non-smooth Variable Projection
In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke's generalized Jacobian of the…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…
This paper addresses constrained smooth saddle-point problems in settings where projection onto the feasible sets is computationally expensive. We bridge the gap between projection-based and projection-free optimization by introducing a…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
It is known that adaptive optimization algorithms represent the key pillar behind the rise of the Machine Learning field. In the Optimization literature numerous studies have been devoted to accelerated gradient methods but only recently…
Beginning with the projectively invariant method for linear programming, interior point methods have led to powerful algorithms for many difficult computing problems, in combinatorial optimization, logic, number theory and non-convex…
In classic robust optimization, it is assumed that a set of possible parameter realizations, the uncertainty set, is modeled in a previous step and part of the input. As recent work has shown, finding the most suitable uncertainty set is in…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
We develop two adaptive discretization algorithms for convex semi-infinite optimization, which terminate after finitely many iterations at approximate solutions of arbitrary precision. In particular, they terminate at a feasible point of…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
Algorithms that solve zero-sum games, multi-objective agent objectives, or, more generally, variational inequality (VI) problems are notoriously unstable on general problems. Owing to the increasing need for solving such problems in machine…
We address composite optimization problems, which consist in minimizing the sum of a smooth and a merely lower semicontinuous function, without any convexity assumptions. Numerical solutions of these problems can be obtained by proximal…
Optimization is an essential component for solving problems in wide-ranging fields. Ideally, the objective function should be designed such that the solution is unique and the optimization problem can be solved stably. However, the…
Time-varying optimization problems are prevalent in various engineering fields, and the ability to solve them accurately in real-time is becoming increasingly important. The prediction-correction algorithms used in smooth time-varying…
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…
We introduce a class of stochastic algorithms for minimizing weakly convex functions over proximally smooth sets. As their main building blocks, the algorithms use simplified models of the objective function and the constraint set, along…
Optimization is a ubiquitous modeling tool and is often deployed in settings which repeatedly solve similar instances of the same problem. Amortized optimization methods use learning to predict the solutions to problems in these settings,…
We study the problem of optimizing nonlinear objective functions over bipartite matchings. While the problem is generally intractable, we provide several efficient algorithms for it, including a deterministic algorithm for maximizing convex…
In practice, optimization tasks have some structure that allows developing new algorithms for every problem with faster convergence rates. Using the structure of optimization tasks, we can propose algorithms with more optimistic convergence…
An algorithm is proposed, analyzed, and tested for solving continuous nonlinear-equality-constrained optimization problems where the objective and constraint functions are defined by expectations or averages over large, finite numbers of…