Related papers: On the Optimality of a Class of LP-based Algorithm…
In [SIAM J. Optim., 2022], the authors introduced a new linear programming (LP) relaxation for K-means clustering. In this paper, we further investigate both theoretical and computational properties of this relaxation. As evident from our…
We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…
Consider the following optimization problem: Given $n \times n$ matrices $A$ and $\Lambda$, maximize $\langle A, U\Lambda U^*\rangle$ where $U$ varies over the unitary group $\mathrm{U}(n)$. This problem seeks to approximate $A$ by a matrix…
This paper studies two fundamental problems in power systems: the economic dispatch problem (EDP) and load shedding. For the EDP, an extension of the problem considering the transmission losses is presented. Because the optimization problem…
This paper studies how to solve semi-infinite polynomial programming (SIPP) problems by semidefinite relaxation method. We first introduce two SDP relaxation methods for solving polynomial optimization problems with finitely many…
Orthogonal collocation methods are direct approaches for solving optimal control problems (OCP). A high solution accuracy is achieved with few optimization variables, making it more favorable for embedded and real-time NMPC applications.…
Packing rings into a minimum number of rectangles is an optimization problem which appears naturally in the logistics operations of the tube industry. It encompasses two major difficulties, namely the positioning of rings in rectangles and…
Recent LLM-driven discoveries have renewed interest in geometric packing problems. In this paper, we study several classes of such packing problems through the lens of modern global nonlinear optimization. Starting from comparatively direct…
In the rectangle stabbing problem, we are given a set $\cR$ of axis-aligned rectangles in $\RR^2$, and the objective is to find a minimum-cardinality set of horizontal and/or vertical lines such that each rectangle is intersected by one of…
We develop polynomial-size LP-relaxations for {\em orienteering} and the {\em regret-bounded vehicle routing problem} (\rvrp) and devise suitable LP-rounding algorithms that lead to various new insights and approximation results for these…
We investigate Learning from Label Proportions (LLP), a partial information setting where examples in a training set are grouped into bags, and only aggregate label values in each bag are available. Despite the partial observability, the…
The question of the existence of a polynomial kernelization of the Vertex Cover Above LP problem has been a longstanding, notorious open problem in Parameterized Complexity. Five years ago, the breakthrough work by Kratsch and Wahlstrom on…
In this paper, we consider the network slicing problem which attempts to map multiple customized virtual network requests (also called services) to a common shared network infrastructure and allocate network resources to meet diverse…
Clustering algorithms have significantly improved along with Deep Neural Networks which provide effective representation of data. Existing methods are built upon deep autoencoder and self-training process that leverages the distribution of…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
Chromatic Correlation Clustering (CCC) generalizes Correlation Clustering by assigning multiple categorical relationships (colors) to edges and imposing chromatic constraints on the clusters. Unlike traditional Correlation Clustering, which…
Recent work on deep clustering has found new promising methods also for constrained clustering problems. Their typically pairwise constraints often can be used to guide the partitioning of the data. Many problems however, feature…
Consider the following variant of the set cover problem. We are given a universe $U=\{1,...,n\}$ and a collection of subsets $\mathcal{C} = \{S_1,...,S_m\}$ where $S_i \subseteq U$. For every element $u \in U$ we need to find a set $\phi(u)…
This paper studies a class of so-called linear semi-infinite polynomial programming (LSIPP) problems. It is a subclass of linear semi-infinite programming problems whose constraint functions are polynomials in parameters and index sets are…
In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of…