Related papers: Relations between Abs-Normal NLPs and MPCCs. Part …
We consider the modified Monge-Kantorovich problem with additional restriction: admissible transport plans must vanish on some fixed functional subspace. Different choice of the subspace leads to different additional properties optimal…
Minimax optimization problems are an important class of optimization problems arising from both modern machine learning and from traditional research areas. We focus on the stability of constrained minimax optimization problems based on the…
We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…
This paper addresses the real structured controllability, stabilizability, and stability radii (RSCR, RSSZR, and RSSR, respectively) of linear systems, which involve determining the distance (in terms of matrix norms) between a (possibly…
The constraint nondegeneracy condition is one of the most relevant and useful constraint qualifications in nonlinear semidefinite programming. It can be characterized in terms of any fixed orthonormal basis of the, let us say,…
This paper considers a bilevel program, which has many applications in practice. To develop effective numerical algorithms, it is generally necessary to transform the bilevel program into a single-level optimization problem. The most…
We show that the training problem of a deep linear neural network under the squared loss admits an exact convex reformulation in a lifted space over a generalized completely positive cone. The reformulation has the same optimal value as the…
We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a…
This paper argues that the judicial use of formal language theory and grammatical inference are invaluable tools in understanding how deep neural networks can and cannot represent and learn long-term dependencies in temporal sequences.…
Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high…
Low rank recovery problems have been a subject of intense study in recent years. While the rank function is useful for regularization it is difficult to optimize due to its non-convexity and discontinuity. The standard remedy for this is to…
Many important modeling tasks in linear regression, including variable selection (in which slopes of some predictors are set equal to zero) and simplified models based on sums or differences of predictors (in which slopes of those…
This paper presents a theoretical overview of a Neural Contraction Metric (NCM): a neural network model of an optimal contraction metric and corresponding differential Lyapunov function, the existence of which is a necessary and sufficient…
In a previous paper [R. Andreani, G. Haeser, L. M. Mito, H. Ram\'irez, T. P. Silveira. First- and second-order optimality conditions for second-order cone and semidefinite programming under a constant rank condition. Mathematical…
Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology design and robot motion planning. MPVCs are difficult problems…
Reinforcement learning (RL) is an effective approach for solving optimal control problems without knowing the exact information of the system model. However, the classical Q-learning method, a model-free RL algorithm, has its limitations,…
In this brief, we consider the constrained optimization problem underpinning model predictive control (MPC). We show that this problem can be decomposed into an unconstrained optimization problem with the same cost function as the original…
This paper addresses two related problems in optimal control. The first investigation consists of compatibility issues between two classical approaches to deriving necessary conditions for optimal control problems with a final target: the…
The paper is devoted to an analysis of a new constraint qualification and a derivation of the strongest existing optimality conditions for nonsmooth mathematical programming problems with equality and inequality constraints in terms of…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…