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In this paper, we consider nonsmooth composite optimization over compact embedded submanifolds defined by nonlinear equality constraints. We propose a feasibility-safeguarded inexact proximal linearized method (FSIPL), which allows…
In this work, the author presents a novel method for finding descent directions shared by two or more differentiable functions defined on the same unconstrained domain space. Then, the author illustrates an alternative Multiple-Gradient…
Hyperparameter tuning is an important task of machine learning, which can be formulated as a bilevel program (BLP). However, most existing algorithms are not applicable for BLP with non-smooth lower-level problems. To address this, we…
Basis pursuit is the problem of finding a vector with smallest $\ell_1$-norm among the solutions of a given linear system of equations. It is a well-known convex relaxation of the sparse affine feasibility problem, where sparse solutions to…
We present a new algorithm for solving optimization problems with objective functions that are the sum of a smooth function and a (potentially) nonsmooth regularization function, and nonlinear equality constraints. The algorithm may be…
In this paper we study general $l_p$ regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the $l_p$…
We study bilevel optimization problems where the lower-level problems are strongly convex and have coupled linear constraints. To overcome the potential non-smoothness of the hyper-objective and the computational challenges associated with…
A fundamental theorem of linear programming states that a feasible linear program is solvable if and only if its objective function is copositive with respect to the recession cone of its feasible set. This paper demonstrates that this…
Hierarchical least-squares programs with linear constraints (HLSP) are a type of optimization problem very common in robotics. Each priority level contains an objective in least-squares form which is subject to the linear constraints of the…
Linearizability has become the de facto correctness specification for implementations of concurrent data structures. While formally verifying such implementations remains challenging, linearizability monitoring has emerged as a promising…
The Symmetric Primal-Dual Symplex Pivot Decision Strategy (spdspds) is a novel iterative algorithm to solve linear programming problems. A symplex pivoting operation is simply an exchange between a basic variable and a non-basic variable,…
Parsimony, including sparsity and low rank, has been shown to successfully model data in numerous machine learning and signal processing tasks. Traditionally, such modeling approaches rely on an iterative algorithm that minimizes an…
The great advances of learning-based approaches in image processing and computer vision are largely based on deeply nested networks that compose linear transfer functions with suitable non-linearities. Interestingly, the most frequently…
This paper is about a machine learning approach based on the multilinear projection of an unknown function (or probability distribution) to be estimated towards a linear (or multilinear) dimensional space E'. The proposal transforms the…
This paper introduces scalable, sampling-based algorithms that optimize trained neural networks with ReLU activations. We first propose an iterative algorithm that takes advantage of the piecewise linear structure of ReLU neural networks…
We study a structured linear program (LP) that emerges in the need of ranking candidates or items in personalized recommender systems. Since the candidate set is only known in real time, the LP also needs to be formed and solved in real…
In this paper, we consider bilevel optimization problem where the lower-level has coupled constraints, i.e. the constraints depend both on the upper- and lower-level variables. In particular, we consider two settings for the lower-level…
A computationally efficient method to solve non-convex programming problems with linear equality constraints is presented. The proposed method is based on a recursively feasible and descending sequential convex programming procedure proven…
A linear programming (LP) based framework is presented for obtaining converses for finite blocklength lossy joint source-channel coding problems. The framework applies for any loss criterion, generalizes certain previously known converses,…
In modern engineering scenarios, there is often a strict upper bound on the number of algorithm iterations that can be performed within a given time limit. This raises the question of optimal algorithmic configuration for a fixed and finite…