Related papers: A Generalized Waist Problem: Optimality Condition …
In this paper we consider a problem, called convex projection, of projecting a convex set onto a subspace. We will show that to a convex projection one can assign a particular multi-objective convex optimization problem, such that the…
We study the problem of partitioning a polygon into the minimum number of subpolygons using cuts in predetermined directions such that each resulting subpolygon satisfies a given width constraint. A polygon satisfies the unit-width…
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…
We outline a new approach for solving optimization problems which enforce triangle inequalities on output variables. We refer to this as metric-constrained optimization, and give several examples where problems of this form arise in machine…
Bilevel optimization has recently regained interest owing to its applications in emerging machine learning fields such as hyperparameter optimization, meta-learning, and reinforcement learning. Recent results have shown that simple…
Newton's problem of the body of minimal aerodynamic resistance is traditionally stated in the class of {\it convex} axially symmetric bodies with fixed length and width. We state and solve the minimal resistance problem in the wider class…
A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a…
The convex feasibility problem asks to find a point in the intersection of a collection of nonempty closed convex sets. This problem is of basic importance in mathematics and the physical sciences, and projection (or splitting) methods…
This paper presents connections between Gromov's work on isoperimetry of waists and Milman's work on the $M$-ellipsoid of a convex body. It is proven that any convex body $K \subseteq \mathbb{R}^n$ has a linear image $\tilde{K} \subseteq…
A wide array of machine learning problems are formulated as the minimization of the expectation of a convex loss function on some parameter space. Since the probability distribution of the data of interest is usually unknown, it is is often…
We investigate several problems in entanglement theory from the perspective of convex optimization. This list of problems comprises (A) the decision whether a state is multi-party entangled, (B) the minimization of expectation values of…
Visibility plays an important role for decision making in cluttered, uncertain environments. This paper considers the problem of identifying optimal hiding spots for an agent against line-of-sight detection by an adversary whose location is…
We introduce an algorithm which can be directly used to feasible and optimum search in linear programming. Starting from an initial point the algorithm iteratively moves a point in a direction to resolve the violated constraints. At the…
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point. While classical first-order gradient descent methods can solve them, they converge very slowly. In this paper, we propose new…
This paper introduces a first-order method for solving optimal powered descent guidance (PDG) problems, that directly handles the nonconvex constraints associated with the maximum and minimum thrust bounds with varying mass and the pointing…
This work addresses arbitrary convex vector optimization problems, which constitute a general framework for multi-criteria decision-making in diverse real-world applications. Due to their complexity, such problems are typically tackled…
We study the problem of representing all distances between $n$ points in $\mathbb R^d$, with arbitrarily small distortion, using as few bits as possible. We give asymptotically tight bounds for this problem, for Euclidean metrics, for…
Bilevel optimization has witnessed a resurgence of interest, driven by its critical role in trustworthy and efficient AI applications. While many recent works have established convergence to stationary points or local minima, obtaining the…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
Barycenter problems encode important geometric information about a metric space. While these problems are typically studied with positive weight coefficients associated to each distance term, more general signed Wasserstein barycenter…