Related papers: Optimality Conditions for Cardinality-Constrained …
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
The linear submodular bandit problem was proposed to simultaneously address diversified retrieval and online learning in a recommender system. If there is no uncertainty, this problem is equivalent to a submodular maximization problem under…
This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
Convex optimization problems with staged structure appear in several contexts, including optimal control, verification of deep neural networks, and isotonic regression. Off-the-shelf solvers can solve these problems but may scale poorly. We…
It is well known that there have been many numerical algorithms for solving nonsmooth minimax problems, numerical algorithms for nonsmooth minimax problems with joint linear constraints are very rare. This paper aims to discuss optimality…
Constrained non-convex optimization problems frequently arise in control applications. Solving such problems is inherently challenging, as existing methods often converge to suboptimal local minima or incur prohibitive computational costs.…
We study randomized algorithms for constrained optimization, in abstract frameworks that include, in strictly increasing generality: convex programming; LP-type problems; violator spaces; and a setting we introduce, consistent spaces. Such…
Minimax optimization problems arises from both modern machine learning including generative adversarial networks, adversarial training and multi-agent reinforcement learning, as well as from tradition research areas such as saddle point…
We model the cardinality-constrained portfolio problem using semidefinite matrices and investigate a relaxation using semidefinite programming. Experimental results show that this relaxation generates tight lower bounds and even achieves…
We provide a formula for the lower bound in the form of $|F| \ge K$, in such a way that the decision version of unweighted non-bipartite matching can be solved in polynomial time. ~The parameter $K$ can vary from instance to instance. We…
We show how the solution to NMPC problems for a special type of input-affine discrete-time systems can be obtained by reformulating the underlying non-convex optimal control problem in terms of a finite number of convex subproblems. The…
We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong…
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice.…
In this article, we build on previous work to present an optimization algorithm for nonlinearly constrained multi-objective optimization problems. The algorithm combines a surrogate-assisted derivative-free trust-region approach with the…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Optimization models with non-convex constraints arise in many tasks in machine learning, e.g., learning with fairness constraints or Neyman-Pearson classification with non-convex loss. Although many efficient methods have been developed…
Financial portfolios are often optimized for maximum profit while subject to a constraint formulated in terms of the Conditional Value-at-Risk (CVaR). This amounts to solving a linear problem. However, in its original formulation this…
A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…