相关论文: A novel approach for bilevel programs based on Wol…

We explore the class of trilevel equilibrium problems with a focus on energy-environmental applications and present a novel single-level reformulation for such problems, based on strong duality. To the best of our knowledge, only one…

We present a blended conditional gradient approach for minimizing a smooth convex function over a polytope P, combining the Frank--Wolfe algorithm (also called conditional gradient) with gradient-based steps, different from away steps and…

Large-scale optimization problems arising from the discretization of problems involving PDEs sometimes admit solutions that can be well approximated by low-rank matrices. In this paper, we will exploit this low-rank approximation property…

Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this paper we address power system problems of bilevel structure,…

We present differentially private (DP) algorithms for bilevel optimization, a problem class that received significant attention lately in various machine learning applications. These are the first algorithms for such problems under standard…

The pursuit of robustness has recently been a popular topic in reinforcement learning (RL) research, yet the existing methods generally suffer from efficiency issues that obstruct their real-world implementation. In this paper, we introduce…

In recent years, bilevel approaches have become very popular to efficiently estimate high-dimensional hyperparameters of machine learning models. However, to date, binary parameters are handled by continuous relaxation and rounding…

We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal…

Practical optimization problems may contain different kinds of difficulties that are often not tractable if one relies on a particular optimization method. Different optimization approaches offer different strengths that are good at…

Gradient methods have become mainstream techniques for Bi-Level Optimization (BLO) in learning and vision fields. The validity of existing works heavily relies on solving a series of approximation subproblems with extraordinarily high…

We consider a multiobjective bilevel optimization problem with vector-valued upper- and lower-level objective functions. Such problems have attracted a lot of interest in recent years. However, so far, scalarization has appeared to be the…

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the…

In this workshop, we present a compact but rigorous introduction to second-order optimality conditions for mathematical programs with equilibrium constraints (MPECs). We start from the classical nonlinear programming template, then explain…

Bilevel optimization problems are a class of challenging optimization problems, which contain two levels of optimization tasks. In these problems, the optimal solutions to the lower level problem become possible feasible candidates to the…

Model predictive control (MPC) has been widely used in many fields, often in hierarchical architectures that combine controllers and decision-making layers at different levels. However, when such architectures are cast as bilevel…

Conditional Gradient algorithms (aka Frank-Wolfe algorithms) form a classical set of methods for constrained smooth convex minimization due to their simplicity, the absence of projection steps, and competitive numerical performance. While…

This paper studies bilevel polynomial optimization in which lower-level constraint functions depend linearly on lower-level variables. We show that such bilevel program can be reformulated as a disjunctive program by using…

Dantzig-Wolfe (DW) decomposition is a well-known technique in mixed-integer programming (MIP) for decomposing and convexifying constraints to obtain potentially strong dual bounds. We investigate cutting planes that can be derived using the…

We present a novel analysis of semidefinite programs (SDPs) with positive duality gaps, i.e. different optimal values in the primal and dual problems. These SDPs are extremely pathological, often unsolvable, and also serve as models of more…

In the rank-constrained optimization problem (RCOP), it minimizes a linear objective function over a prespecified closed rank-constrained domain set and $m$ generic two-sided linear matrix inequalities. Motivated by the Dantzig-Wolfe (DW)…