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Stochastic convex optimization problems with expectation constraints (SOECs) are encountered in statistics and machine learning, business, and engineering. In data-rich environments, the SOEC objective and constraints contain expectations…
We propose a new calculus SCL(EQ) for first-order logic with equality that only learns non-redundant clauses. Following the idea of CDCL (Conflict Driven Clause Learning) and SCL (Clause Learning from Simple Models) a ground literal model…
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…
In this paper, a well-posed simultaneous space-time First Order System Least Squares formulation is constructed of the instationary incompressible Stokes equations with slip boundary conditions. As a consequence of this well-posedness, the…
Recent years have witnessed the success of dictionary learning (DL) based approaches in the domain of pattern classification. In this paper, we present an efficient structured dictionary learning (ESDL) method which takes both the diversity…
Nowadays, numerous services based on large-scale distributed systems have been developed to boost the convenience of human life. On the other side, it becomes a significant challenge to ensure the correctness and properties of these systems…
We introduce a class of first-order methods for smooth constrained optimization that are based on an analogy to non-smooth dynamical systems. Two distinctive features of our approach are that (i) projections or optimizations over the entire…
Signal Temporal Logic (STL) is expressive formal language that specifies spatio-temporal requirements in robotics. Its quantitative robustness semantics can be easily integrated with optimization-based control frameworks. However, STL…
In this paper, we study a class of stochastic and finite-sum convex optimization problems with deterministic constraints. Existing methods typically aim to find an $\epsilon$-$expectedly\ feasible\ stochastic\ optimal$ solution, in which…
Signal Temporal Logic (STL) is a powerful formal language for specifying real-time specifications of Cyber-Physical Systems (CPS). Transforming specifications written in natural language into STL formulas automatically has attracted…
We consider stochastic unconstrained bilevel optimization problems when only the first-order gradient oracles are available. While numerous optimization methods have been proposed for tackling bilevel problems, existing methods either tend…
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied…
We use the linear scalar SDE as a test problem to show that it is possible to construct almost sure stable first-order weak balanced schemes based on the addition of stabilizing functions to the drift terms. Then, we design balanced schemes…
The sequential semantics of many concurrent data structures, such as stacks and queues, inevitably lead to memory contention in parallel environments, thus limiting scalability. Semantic relaxation has the potential to address this issue,…
We exploit analogies between first-order algorithms for constrained optimization and non-smooth dynamical systems to design a new class of accelerated first-order algorithms for constrained optimization. Unlike Frank-Wolfe or projected…
This paper presents an up-to-date and refined version of the SCL calculus for first-order logic without equality. The refinement mainly consists of the following two parts: First, we incorporate a stronger notion of regularity into…
As large pre-trained language models become increasingly critical to natural language understanding (NLU) tasks, their substantial computational and memory requirements have raised significant economic and environmental concerns. Addressing…
The first-order system LL* (FOSLL*) approach for general second-order elliptic partial differential equations was proposed and analyzed in [10], in order to retain the full efficiency of the L2 norm first-order system least-squares (FOSLS)…
Large-scale pretrained language models have achieved compelling performance in a wide range of language understanding and information retrieval tasks. Knowledge distillation offers an opportunity to compress a large language model to a…
Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis…