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This paper studies a multiobjective bilevel optimization problem where each objective is a fractional function. By reformulating the problem into a single-level one, we establish refined necessary and sufficient optimality conditions. These…

Due to the hierarchical structure of many machine learning problems, bilevel programming is becoming more and more important recently, however, the complicated correlation between the inner and outer problem makes it extremely challenging…

Although Minimum Distance Parsing (MDP) offers a theoretically attractive solution to the problem of extragrammaticality, it is often computationally infeasible in large scale practical applications. In this paper we present an alternative…

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems which has some important applications. It is…

The application of the Reformulation Linearization Technique (RLT) to the Quadratic Assignment Problem (QAP) leads to a tight linear relaxation with huge dimensions that is hard to solve. Previous works found in the literature show that…

Dynamic optimization of mean and variance in Markov decision processes (MDPs) is a long-standing challenge caused by the failure of dynamic programming. In this paper, we propose a new approach to find the globally optimal policy for…

This paper presents a new approach to quadrify a polynomial programming problem, i.e. reduce the polynomial program to a quadratic program, before solving it. The proposed approach, QUAD-RLT, exploits the Reformulation-Linearization…

We study the policy testing problem in discounted Markov decision processes (MDPs) in the fixed-confidence setting under a generative model with static sampling. The goal is to decide whether the value of a given policy exceeds a specified…

Robust Markov decision processes (MDPs) provide a general framework to model decision problems where the system dynamics are changing or only partially known. Efficient methods for some \texttt{sa}-rectangular robust MDPs exist, using its…

In this paper, we propose a procedure for designing controlled test problems for single-objective bilevel optimization. The construction procedure is flexible and allows its user to control the different complexities that are to be included…

We consider the problem of learning the optimal policy for infinite-horizon Markov decision processes (MDPs). For this purpose, some variant of Stochastic Mirror Descent is proposed for convex programming problems with Lipschitz-continuous…

It is one of the most challenging problems in applied mathematics to approximatively solve high-dimensional partial differential equations (PDEs). In particular, most of the numerical approximation schemes studied in the scientific…

This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…

In this paper, we study the learning of safe policies in the setting of reinforcement learning problems. This is, we aim to control a Markov Decision Process (MDP) of which we do not know the transition probabilities, but we have access to…

This paper introduces a computationally efficient method that converges globally to B-stationary points of mathematical programs with equilibrium constraints (MPECs). B-stationarity is necessary for optimality and means that no feasible…

This paper presents a canonical duality approach for solving a general topology optimization problem of nonlinear elastic structures. By using finite element method, this most challenging problem can be formulated as a mixed integer…

In this technical report, we compare multiple reformulation techniques and solvers that can be used with the Julia package BilevelJuMP. We focus on the special case of Hyperparameter Tuning for Support Vector Regression. We describe a…

Approximate linear programming (ALP) is an efficient approach to solving large factored Markov decision processes (MDPs). The main idea of the method is to approximate the optimal value function by a set of basis functions and optimize…

Semidefinite Programming (SDP) provides tight lower bounds for Optimal Power Flow problems. However, solving large-scale SDP problems requires exploiting sparsity. In this paper, we experiment several clique decomposition algorithms that…

This paper studies decentralized bilevel optimization, in which multiple agents collaborate to solve problems involving nested optimization structures with neighborhood communications. Most existing literature primarily utilizes gradient…