Related papers: Two-Commodity Flow is Equivalent to Linear Program…
Cutting and packing problems are fundamental in manufacturing and logistics, as they aim to minimize waste and improve efficiency. The Cutting Stock Problem (CSP) concerns material cutting, whereas the Bin Packing Problem (BPP) concerns…
We investigate the complexity of training a two-layer ReLU neural network with weight decay regularization. Previous research has shown that the optimal solution of this problem can be found by solving a standard cone-constrained convex…
Strip packing is a classical packing problem, where the goal is to pack a set of rectangular objects into a strip of a given width, while minimizing the total height of the packing. The problem has multiple applications, e.g. in scheduling…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
In quantum computation we are given a finite set of gates and we have to perform a desired operation as a product of them. The corresponding computational problem is approximating an arbitrary unitary as a product in a topological…
Coflow is a network abstraction used to represent communication patterns in data centers. The coflow scheduling problem in large data centers is one of the most important $NP$-hard problems. Many previous studies on coflow scheduling mainly…
Global optimization problems with a quasi-concave objective function and linear constraints are studied. We point out that various other classes of global optimization problems can be expressed in this way. We present two algorithms, which…
Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem -- the all-or-nothing multicommodity flow (ANF) problem -- in arbitrary directed graphs and in the…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
In many power system optimization problems, we observe that only a small fraction of the line flow constraints ever become active at the optimal solution, despite variations in the load profile and generation costs. This observation has…
We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…
Many nonlinear optimal control and optimization problems involve constraints that combine continuous dynamics with discrete logic conditions. Standard approaches typically rely on mixed-integer programming, which introduces scalability…
In this paper we propose a new approach for developing a proof that P=NP. We propose to use a polynomial-time reduction of a NP-complete problem to Linear Programming. Earlier such attempts used polynomial-time transformation which is a…
We prove that the standard gradient flow in parameter space that underlies many training algorithms in deep learning can be continuously deformed into an adapted gradient flow which yields (constrained) Euclidean gradient flow in output…
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…
We study the problem of computing a minimum equivalent digraph (also known as the problem of computing a strong transitive reduction) and its maximum objective function variant, with two types of extensions. First, we allow to declare a set…
In the area of parameterized complexity, to cope with NP-Hard problems, we introduce a parameter k besides the input size n, and we aim to design algorithms (called FPT algorithms) that run in O(f(k)n^d) time for some function f(k) and…
In this paper, a two-phase quasi-Newton scheme is proposed for solving an unconstrained optimization problem. The global convergence property of the scheme is provided under mild assumptions. The superlinear rate of the scheme is also…
We analyze the bit complexity of efficient algorithms for fundamental optimization problems, such as linear regression, $p$-norm regression, and linear programming (LP). State-of-the-art algorithms are iterative, and in terms of the number…
We study the problem of minimizing total completion time on parallel machines subject to varying processing capacity. In this paper, we develop an approximation scheme for the problem under the data stream model where the input data is…