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Large Language Models (LLMs) are increasingly embedded in enterprise workflows, yet their performance remains highly sensitive to prompt design. Automatic Prompt Optimization (APO) seeks to mitigate this instability, but existing approaches…
We employ chordal decomposition to reformulate a large and sparse semidefinite program (SDP), either in primal or dual standard form, into an equivalent SDP with smaller positive semidefinite (PSD) constraints. In contrast to previous…
The primal-dual algorithm recently proposed by Chambolle & Pock (abbreviated as CPA) for structured convex optimization is very efficient and popular. It was shown by Chambolle & Pock in \cite{CP11} and also by Shefi & Teboulle in…
The online randomized primal-dual method has widespread applications in online algorithm design and analysis. A key challenge is identifying an appropriate function space, $F$, in which we search for an optimal updating function $f \in F$…
We consider the convex-concave saddle point problem $\min_{\mathbf{x}}\max_{\mathbf{y}}\Phi(\mathbf{x},\mathbf{y})$, where the decision variables $\mathbf{x}$ and/or $\mathbf{y}$ subject to a multi-block structure and affine coupling…
We propose a fast algorithm for computing the GMM estimator in the BLP demand model (Berry, Levinsohn, and Pakes, 1995). Inspired by nested pseudo-likelihood methods for dynamic discrete choice models, our approach avoids repeatedly solving…
We propose a novel methodology for solving a two-stage adjustable robust convex optimisation problem with a general (proximable) convex objective function and constraints defined by sum-of-squares (SOS) convex polynomials. These problems…
Selecting the fastest algorithm for a specific signal/image processing task is a challenging question. We propose an approach based on the Performance Estimation Problem framework that numerically and automatically computes the worst-case…
We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…
We consider the following two deterministic inventory optimization problems over a finite planning horizon $T$ with non-stationary demands. (a) Submodular Joint Replenishment Problem: This involves multiple item types and a single retailer…
We investigate the sequential competitive facility location problem (SCFLP) under partially binary rule where two companies sequentially open a limited number of facilities to maximize their market shares, requiring customers to patronize,…
A number of problems in relational Artificial Intelligence can be viewed as Stochastic Constraint Optimization Problems (SCOPs). These are constraint optimization problems that involve objectives or constraints with a stochastic component.…
Key challenges in running a retail business include how to select products to present to consumers (the assortment problem), and how to price products (the pricing problem) to maximize revenue or profit. Instead of considering these…
We study offline reinforcement learning (RL) with linear MDPs under the infinite-horizon discounted setting which aims to learn a policy that maximizes the expected discounted cumulative reward using a pre-collected dataset. Existing…
Capturing users' precise preferences is a fundamental problem in large-scale recommender system. Currently, item-based Collaborative Filtering (CF) methods are common matching approaches in industry. However, they are not effective to model…
Many techniques for real-time trajectory optimization and control require the solution of optimization problems at high frequencies. However, ill-conditioning in the optimization problem can significantly reduce the speed of first-order…
Structural pruning techniques are essential for deploying multimodal large language models (MLLMs) across various hardware platforms, from edge devices to cloud servers. However, current pruning methods typically determine optimal…
First-order primal-dual methods are appealing for their low memory overhead, fast iterations, and effective parallelization. However, they are often slow at finding high accuracy solutions, which creates a barrier to their use in…
Primal-dual methods in online optimization give several of the state-of-the art results in both of the most common models: adversarial and stochastic/random order. Here we try to provide a more unified analysis of primal-dual algorithms to…
Today's global supply chains face growing challenges due to rapidly changing market conditions, increased network complexity and inter-dependency, and dynamic uncertainties in supply, demand, and other factors. To combat these challenges,…