Related papers: Relaxation strength for multilinear optimization: …
We study a posterior sampling approach to efficient exploration in constrained reinforcement learning. Alternatively to existing algorithms, we propose two simple algorithms that are more efficient statistically, simpler to implement and…
It is well known that the iterates of an averaged nonexpansive mapping may only converge weakly to fixed point. A celebrated result by Baillon, Bruck, and Reich from 1978 yields strong convergence in the presence of linearity. In this…
We study decision rule approximations for generic multi-stage robust linear optimization problems. We consider linear decision rules for the case when the objective coefficients, the recourse matrices, and the right-hand sides are…
The Optimal Power Flow (OPF) problem can be reformulated as a nonconvex Quadratically Constrained Quadratic Program (QCQP). There is a growing body of work on the use of semidefinite programming relaxations to solve OPF. The relaxation is…
We prove a relaxation result for a quasi-convex bulk integral functional with variable exponent growth in a suitable space of bounded variation type. A key tool is a decomposition under mild assumptions of the energy into absolutely…
We present a linear cutting-plane relaxation approach that rapidly proves tight lower bounds for the Alternating Current Optimal Power Flow Problem (ACOPF). Our method leverages outer-envelope linear cuts for well-known second-order cone…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
This paper develops a novel second order cone relaxation of the semidefinite programming formulation of optimal power flow, that does not imply the `angle relaxation'. We build on a technique developed by Kim et al., extend it for complex…
The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…
The notion of tail adversarial stability has been proven useful in obtaining limit theorems for tail dependent time series. Its implication and advantage over the classical strong mixing framework has been examined for max-linear processes,…
Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…
Projection-based iterative methods for solving large over-determined linear systems are well-known for their simplicity and computational efficiency. It is also known that the correct choice of a sketching procedure (i.e., preprocessing…
Computing at the exascale level is expected to be affected by a significantly higher rate of faults, due to increased component counts as well as power considerations. Therefore, current day numerical algorithms need to be reexamined as to…
In this paper, we consider a theoretical framework for comparing branch-and-bound with classical lift-and-project hierarchies. We simplify our analysis of streamlining the definition of branch-and-bound. We introduce "skewed $k$-trees"…
Algebraic multigrid (AMG) methods derive their optimal efficiency from the interplay between a relaxation process and a corresponding coarse grid correction. In many standard formulations, relaxation and coarse-graining are analyzed and…
In this paper, we will present a generalization for a minimization problem from I. Daubechies, M. Defrise, and C. Demol [3]. This generalization is useful for solving many practical problems in which more than one constraint are involved.…
The high-energy evolution of Wilson line operators, which at leading order is described by the Balitsky-JIMWLK equations, receives large radiative corrections enhanced by single and double collinear logarithms at next-to-leading order and…
Semidefinite relaxations of polynomial optimization have become a central tool for addressing the non-convex optimization problems over non-commutative operators that are ubiquitous in quantum information theory and, more in general,…
This work builds on our recent work on a distributed optimization algorithm for graphs with directed unreliable communications. We show its linear convergence when we take either the proximal of each function or an affine minorant for when…
The paper is devoted to the relaxation and integral representation in the space of functions of bounded variation for an integral energy arising from optimal design problems. The presence of a perimeter penalization is also considered in…