Related papers: Starting CLuP with polytope relaxation
The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…
Finding locally optimal solutions for max-cut and max-$k$-cut are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in…
Detectability of failures of linear programming (LP) decoding and its potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the LP problem. In this paper, we make a…
This paper introduces a new global optimization algorithm for solving the generalized linear multiplicative problem (GLMP). The algorithm starts by introducing $\bar{p}$ new variables and applying a logarithmic transformation to convert the…
We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives…
We propose a general model-free strategy for feedback control design of turbulent flows. This strategy called 'machine learning control' (MLC) is capable of exploiting nonlinear mechanisms in a systematic unsupervised manner. It relies on…
We consider the reinforcement learning problem for the constrained Markov decision process (CMDP), which plays a central role in satisfying safety or resource constraints in sequential learning and decision-making. In this problem, we are…
Linear Programming (LP) is widely applied in industry and is a key component of various other mathematical problem-solving techniques. Recent work introduced an LP compiler translating polynomial-time, polynomial-space algorithms into…
Chordal decomposition techniques are used to reduce large structured positive semidefinite matrix constraints in semidefinite programs (SDPs). The resulting equivalent problem contains multiple smaller constraints on the nonzero blocks (or…
Multiple patterning lithography has been widely adopted in advanced technology nodes of VLSI manufacturing. As a key step in the design flow, multiple patterning layout decomposition (MPLD) is critical to design closure. Due to the…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
Machine learning has become a central research area, with increasing attention devoted to explainable clustering, also known as conceptual clustering, which is a knowledge-driven unsupervised learning paradigm that partitions data into…
Resilience is one of the key algorithmic problems underlying various forms of reverse data management (such as view maintenance, deletion propagation, and various interventions for fairness): What is the minimal number of tuples to delete…
Semidefinite programming (SDP) is widely acknowledged as one of the most effective methods for deriving the tightest lower bounds of the optimal power flow (OPF) problems. In this paper, an enhanced semidefinite relaxation model that…
We propose a novel flexible-step model predictive control algorithm for unknown linear time-invariant discrete-time systems. The goal is to asymptotically stabilize the system without relying on a pre-collected dataset that describes its…
We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow…
In unsupervised feature learning, sample specificity based methods ignore the inter-class information, which deteriorates the discriminative capability of representation models. Clustering based methods are error-prone to explore the…
To address feasibility issues in model predictive control (MPC), most implementations relax state constraints by using slack variables and adding a penalty to the cost. We propose an alternative strategy: relaxing the initial state…
A recent trend in parameterized algorithms is the application of polytope tools (specifically, LP-branching) to FPT algorithms (e.g., Cygan et al., 2011; Narayanaswamy et al., 2012). However, although interesting results have been achieved,…
In this work we propose a single rounding algorithm for the fractional solutions of the standard LP relaxation for $k$-clustering. As a starting point, we obtain an iterative rounding $(\frac{3^p + 1}{2})$-Lagrangian Multiplier-Perserving…