Related papers: Packing Ovals in Optimized Regular Polygons
Porous and heterogeneous materials are found in many applications from composites, membranes, chemical reactors, and other engineered materials to biological matter and natural subsurface structures. In this work we propose an integrated…
We consider methods for finding a simple polygon of minimum (Min-Area) or maximum (Max-Area) possible area for a given set of points in the plane. Both problems are known to be NP-hard; at the center of the recent CG Challenge, practical…
We revisit a standard polygon containment problem: given a convex $k$-gon $P$ and a convex $n$-gon $Q$ in the plane, find a placement of $P$ inside $Q$ under translation and rotation (if it exists), or more generally, find the largest copy…
Quadratic constrained quadratic programming problems often occur in various fields such as engineering practice, management science, and network communication. This article mainly studies a non convex quadratic programming problem with…
Entropic regularization is quickly emerging as a new standard in optimal transport (OT). It enables to cast the OT computation as a differentiable and unconstrained convex optimization problem, which can be efficiently solved using the…
We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…
We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different…
This work presents a unified framework that combines global approximations with locally built models to handle challenging nonconvex and nonsmooth composite optimization problems, including cases involving extended real-valued functions. We…
Optimized Pulse Patterns (OPPs) are gaining increasing popularity in the power electronics community over the well-studied pulse width modulation due to their inherent ability to provide the switching instances that optimize current…
The article demonstrates rather general approach to problems of discrete geometry: treat them as global optimization problems to be solved by one of general purpose solver implementing branch-and-bound algorithm (B&B). This approach may be…
The problem of packing boxes into a large box is often a part of a larger problem. For example in furniture supply chain applications, one needs to decide what trucks to use to transport furniture between production sites and distribution…
We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…
Let $\mathcal{T}$ be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles,…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…
Ordinal Embedding places n objects into R^d based on comparisons such as "a is closer to b than c." Current optimization-based approaches suffer from scalability problems and an abundance of low quality local optima. We instead consider a…
Moser asked whether the collection of rectangles of dimensions 1 x 1/2, 1/2 x 1/3, 1/3 x 1/4, ..., whose total area equals 1, can be packed into the unit square without overlap, and whether the collection of squares of side lengths 1/2,…
This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…
We consider the problem of projecting a convex set onto a subspace, or equivalently formulated, the problem of computing a set obtained by applying a linear mapping to a convex feasible set. This includes the problem of approximating convex…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…