相关论文: Bundle-based pruning in the max-plus curse of dime…

In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…

We present a general method for obtaining strong bounds for discrete optimization problems that is based on a concept of branching duality. It can be applied when no useful integer programming model is available, and we illustrate this with…

When deploying pre-trained neural network models in real-world applications, model consumers often encounter resource-constraint platforms such as mobile and smart devices. They typically use the pruning technique to reduce the size and…

One powerful technique to solve NP-hard optimization problems in practice is branch-and-reduce search---which is branch-and-bound that intermixes branching with reductions to decrease the input size. While this technique is known to be very…

The Maximum Cut (MaxCut) problem is NP-Complete, and obtaining its optimal solution is NP-hard in the worst case. As a result, heuristic-based algorithms are commonly used, though their design often requires significant domain expertise.…

Finding a maximum independent set is a fundamental NP-hard problem that is used in many real-world applications. Given an unweighted graph, this problem asks for a maximum cardinality set of pairwise non-adjacent vertices. Some of the most…

Semidefinite programming is a powerful tool in the design and analysis of approximation algorithms for combinatorial optimization problems. In particular, the random hyperplane rounding method of Goemans and Williamson has been extensively…

Deep Neural Networks are highly over-parameterized and the size of the neural networks can be reduced significantly after training without any decrease in performance. One can clearly see this phenomenon in a wide range of architectures…

This paper presents a novel transformation-proximal bundle algorithm for multistage adaptive robust optimization problems. By partitioning recourse decisions into state and control decisions, the proposed algorithm applies affine control…

The main goal of this paper is to develop uniformly optimal first-order methods for convex programming (CP). By uniform optimality we mean that the first-order methods themselves do not require the input of any problem parameters, but can…

The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage…

With the rise of smartphones and the internet-of-things, data is increasingly getting generated at the edge on local, personal devices. For privacy, latency and energy saving reasons, this shift is causing machine learning algorithms to…

In this contribution we present a new computational method for coupled bulk-surface problems on time-dependent domains. The method is based on a space-time formulation using discontinuous piecewise linear elements in time and continuous…

An efficient approach for the construction of separable approximations of optimal value functions from interconnected optimal control problems is presented. The approach is based on assuming decaying sensitivities between subsystems,…

The linear programming (LP) approach is, together with value iteration and policy iteration, one of the three fundamental methods to solve optimal control problems in a dynamic programming setting. Despite its simple formulation,…

We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…

The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…

We present PFNN, a penalty-free neural network method, to efficiently solve a class of second-order boundary-value problems on complex geometries. To reduce the smoothness requirement, the original problem is reformulated to a weak form so…

We propose a new formulation for the bundle adjustment problem which relies on nullspace marginalization of landmark variables by QR decomposition. Our approach, which we call square root bundle adjustment, is algebraically equivalent to…