Related papers: Concave Generalized Flows with Applications to Mar…
The generalized alternating direction method of multipliers (ADMM) of Xiao et al. [{\tt Math. Prog. Comput., 2018}] aims at the two-block linearly constrained composite convex programming problem, in which each block is in the form of…
Solution methods for generalized Nash equilibrium have been dominated by variational inequalities and complementarity problems. Since these approaches fundamentally rely on the sufficiency of first-order optimality conditions for the…
The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination…
We give a new, flow-type convex program describing equilibrium solutions to linear Arrow-Debreu markets. Whereas convex formulations were previously known [Nenakov, Primak 83; Jain 07; Cornet '89], our program exhibits several new features.…
Over the last decade, combinatorial algorithms have been obtained for exactly solving several nonlinear convex programs. We first provide a formal context to this activity by introducing the notion of {\em rational convex programs} -- this…
This paper researches combinatorial algorithms for the multi-commodity flow problem. We relax the capacity constraints and introduce a penalty function $h$ for each arc. If the flow exceeds the capacity on arc $a$, arc $a$ would have a…
There is a wealth of combinatorial algorithms for classical min-cost flow problems and their simpler variants like max flow or shortest path problems. It is well-known that many of these algorithms are related to the Simplex method and the…
We consider the online unrelated-machine load balancing problem with recourse, where the algorithm is allowed to re-assign prior jobs. We give a $(2+\epsilon)$-competitive algorithm for the problem with $O_\epsilon(\log n)$ amortized…
We propose a decomposition framework for the parallel optimization of the sum of a differentiable function and a (block) separable nonsmooth, convex one. The latter term is typically used to enforce structure in the solution as, for…
We propose a globally convergent Gauss-Newton algorithm for finding a local optimal solution of a non-convex and possibly non-smooth optimization problem. The algorithm that we present is based on a Gauss-Newton-type iteration for the…
In this paper we present a unifying framework for continuous optimization methods grounded in the concept of generalized convexity. Utilizing the powerful theory of $\Phi$-convexity, we propose a conceptual algorithm that extends the…
We consider projection algorithms for solving (nonconvex) feasibility problems in Euclidean spaces. Of special interest are the Method of Alternating Projections (MAP) and the Douglas-Rachford or Averaged Alternating Reflection Algorithm…
We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with $n$ nodes and $m$ edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair…
Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer $L$, an {\em $L$-bounded flow} is a flow between $s$ and $t$ that can be decomposed into paths of length at most $L$. In the {\em maximum $L$-bounded flow…
This paper studies first-order algorithms for solving fully composite optimization problems over convex and compact sets. We leverage the structure of the objective by handling its differentiable and non-differentiable components…
This paper studies the expressive power of artificial neural networks with rectified linear units. In order to study them as a model of real-valued computation, we introduce the concept of Max-Affine Arithmetic Programs and show equivalence…
Continuous normalizing flows are known to be highly expressive and flexible, which allows for easier incorporation of large symmetries and makes them a powerful computational tool for lattice field theories. Building on previous work, we…
Machine Learning models incorporating multiple layered learning networks have been seen to provide effective models for various classification problems. The resulting optimization problem to solve for the optimal vector minimizing the…
We consider a multi-block separable convex optimization problem with the linear constraints, where the objective function is the sum of m individual convex functions without overlapping variables. The linearized version of the generalized…
Multi-region segmentation algorithms often have the onus of incorporating complex anatomical knowledge representing spatial or geometric relationships between objects, and general-purpose methods of addressing this knowledge in an…