Related papers: Validation of a recently proposed strongly polynom…
Existing value function approximation methods have been successfully used in many applications, but they often lack useful a priori error bounds. We propose a new approximate bilinear programming formulation of value function approximation,…
A sparse linear programming (SLP) problem is a linear programming problem equipped with a sparsity (or cardinality) constraint, which is nonconvex and discontinuous theoretically and generally NP-hard computationally due to the…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This paper is aimed to prove the strong duality theorem for continuous-time linear programming problems in which the coefficients are assumed to be piecewise continuous functions. The previous paper proved the strong duality theorem for the…
In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time…
The existence of strongly polynomial-time algorithm for linear programming is a cross-century international mathematical problem, whose breakthrough will solve a major theoretical crisis for the development of artificial intelligence. In…
We present the first near optimal approximation schemes for the maximum weighted (uncapacitated or capacitated) $b$--matching problems for non-bipartite graphs that run in time (near) linear in the number of edges. For any…
We propose and study a weakly convergent variant of the forward--backward algorithm for solving structured monotone inclusion problems. Our algorithm features a per-iteration deviation vector which provides additional degrees of freedom.…
Consider a polynomial optimization problem. Adding polynomial equations generated by the Fritz John conditions to the constraint set does not change the optimal value. As proved in [arXiv:2205.04254 (2022)], the objective polynomial has…
We consider continuous linear programs over a continuous finite time horizon $T$, with a constant coefficient matrix, linear right hand side functions and linear cost coefficient functions, where we search for optimal solutions in the space…
We define a variant of k-of-n testing that we call conservative k-of-n testing. We present a polynomial-time, combinatorial algorithm for the problem of maximizing throughput of conservative k-of-n testing, in a parallel setting. This…
We consider a linear iterative solver for large scale linearly constrained quadratic minimization problems that arise, for example, in optimization with PDEs. By a primal-dual projection (PDP) iteration, which can be interpreted and…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
We present new deterministic algorithms for several cases of the maximum rank matrix completion problem (for short matrix completion), i.e. the problem of assigning values to the variables in a given symbolic matrix as to maximize the…
We study the shared processor scheduling problem with a single shared processor where a unit time saving (weight) obtained by processing a job on the shared processor depends on the job. A polynomial-time optimization algorithm has been…
Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…
An algorithm for a family of self-starting high-order implicit time integration schemes with controllable numerical dissipation is proposed for both linear and nonlinear transient problems. This work builds on the previous works of the…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…