Related papers: A warmstarting technique for general conic optimiz…
Approximate combinatorial optimization is a promising use case for quantum computers. The quantum optimization algorithms often employ a fixed ansatz that evolves an unbiased initial state towards states with better values of the optimand,…
This paper presents an initialization method that can approximate a given approximate Ising model with a high degree of accuracy using a factorization machine (FM), a machine learning model. The construction of an Ising models using an FM…
In this work, we introduce an interior-point method that employs tensor decompositions to efficiently represent and manipulate the variables and constraints of semidefinite programs, targeting problems where the solutions may not be…
The atomic norm provides a generalization of the $\ell_1$-norm to continuous parameter spaces. When applied as a sparse regularizer for line spectral estimation the solution can be obtained by solving a convex optimization problem. This…
The effect on the convergence of warm starting the projected Gauss-Seidel solver for nonsmooth discrete element simulation of granular matter are investigated. It is found that the computational performance can be increased by a factor 2 to…
We provide improved complexity results for symmetric primal--dual interior-point algorithms in conic optimization. The results follow from new uniform bounds on a key complexity measure for primal--dual metrics at pairs of primal and dual…
In this paper we present the Warm-starting Dynamic Thresholding algorithm, developed using dynamic programming, for a variant of the standard online selection problem. The problem allows job positions to be either free or already occupied…
An interior point method for the structural topology optimization is proposed. The linear systems arising in the method are solved by the conjugate gradient method preconditioned by geometric multigrid. The resulting method is then compared…
Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided…
Cold-start exploration is a core challenge in large-scale recommender systems: new or data-sparse items must receive traffic to estimate value, but over-exploration harms users and wastes impressions. In practice, Thompson Sampling (TS) is…
We propose a primal-dual interior-point method (IPM) with convergence to second-order stationary points (SOSPs) of nonlinear semidefinite optimization problems, abbreviated as NSDPs. As far as we know, the current algorithms for NSDPs only…
We consider a continuous-time optimization method based on a dynamical system, where a massive particle starting at rest moves in the conservative force field generated by the objective function, without any kind of friction. We formulate a…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in the primal variable, we develop the first stochastic restart scheme for this…
Thermodynamic computing harnesses the relaxation dynamics of physical systems to perform matrix operations. A key limitation of such approaches is the often long thermalization time required for the system to approach equilibrium with…
In this paper, we define a new, special second order cone as a type-$k$ second order cone. We focus on the case of $k=2$, which can be viewed as SOCO with an additional {\em complicating variable}. For this new problem, we develop the…
In this paper we present a novel numerical method for computing local minimizers of twice smooth differentiable non-linear programming (NLP) problems. So far all algorithms for NLP are based on either of the following three principles:…
We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…
Hyperparameter optimization is both a practical issue and an interesting theoretical problem in training of deep architectures. Despite many recent advances the most commonly used methods almost universally involve training multiple and…
This paper addresses the problem of safe optimization under a single smooth constraint, a scenario that arises in diverse real-world applications such as robotics and autonomous navigation. The objective of safe optimization is to solve a…