相关论文: Two-stage and Lagrangian Dual Decision Rules for M…

We propose a modified primal-dual method for general convex optimization problems with changing constraints. We obtain properties of Lagrangian saddle points for these problems which enable us to establish convergence of the proposed…

Adaptive robust optimization problems have received significant attention in recent years, but remain notoriously difficult to solve when recourse decisions are discrete in nature. In this paper, we propose new reformulation techniques for…

We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve…

We study two-stage distributionally robust optimization (DRO) problems with decision-dependent information discovery (DDID) wherein (a portion of) the uncertain parameters are revealed only if an (often costly) investment is made in the…

By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…

Recently, there has been a growing interest in distributionally robust optimization (DRO) as a principled approach to data-driven decision making. In this paper, we consider a distributionally robust two-stage stochastic optimization…

Learning to Optimize (L2O) approaches, including algorithm unrolling, plug-and-play methods, and hyperparameter learning, have garnered significant attention and have been successfully applied to the Alternating Direction Method of…

We consider the penalized distributionally robust optimization (DRO) problem with a closed, convex uncertainty set, a setting that encompasses learning using $f$-DRO and spectral/$L$-risk minimization. We present Drago, a stochastic…

The use of Lagrangian cuts proves effective in enhancing the lower bound of the master problem within the execution of benders-type algorithms, particularly in the context of two-stage stochastic programs. However, even the process of…

Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…

Two-stage risk-averse distributionally robust optimization (DRO) problems are ubiquitous across many engineering and business applications. Despite their promising resilience, two-stage DRO problems are generally computationally…

This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented…

Two-stage adaptive robust optimization (ARO) is a powerful approach for planning under uncertainty, balancing first-stage decisions with recourse decisions made after uncertainty is realized. To account for uncertainty, modelers typically…

Constrained optimization is popularly seen in reinforcement learning for addressing complex control tasks. From the perspective of dynamic system, iteratively solving a constrained optimization problem can be framed as the temporal…

Robust optimization is an established framework for modeling optimization problems with uncertain parameters. While static robust optimization is often criticized for being too conservative, two-stage (or adjustable) robust optimization…

We consider Lagrangian duality based approaches to design and analyze algorithms for online energy-efficient scheduling. First, we present a primal-dual framework. Our approach makes use of the Lagrangian weak duality and convexity to…

The paper studies a distributed constrained optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local…

We consider the problem of distributionally robust multimodal machine learning. Existing approaches often rely on merging modalities on the feature level (early fusion) or heuristic uncertainty modeling, which downplays modality-aware…

Lagrangian duality in mixed integer optimization is a useful framework for problems decomposition and for producing tight lower bounds to the optimal objective, but in contrast to the convex counterpart, it is generally unable to produce…

Adaptive robust optimization (ARO) is a well-known technique to deal with the parameter uncertainty in optimization problems. While the ARO framework can actually be borrowed to solve some special problems without uncertain parameters, such…