Related papers: Inverse optimization problems with multiple weight…
In this chapter, we are concerned with inverse optimal control problems, i.e., optimization models which are used to identify parameters in optimal control problems from given measurements. Here, we focus on linear-quadratic optimal control…
In this work, we propose a novel inverse reinforcement learning (IRL) algorithm for constrained Markov decision process (CMDP) problems. In standard IRL problems, the inverse learner or agent seeks to recover the reward function of the MDP,…
We survey $k$-best enumeration problems and the algorithms for solving them, including in particular the problems of finding the $k$ shortest paths, $k$ smallest spanning trees, and $k$ best matchings in weighted graphs.
We consider the problem of maximizing an unknown function over a compact and convex set using as few observations as possible. We observe that the optimization of the function essentially relies on learning the induced bipartite ranking…
Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one. Assuming that the homology is defined with integer…
In classical inverse linear optimization, one assumes a given solution is a candidate to be optimal. Real data is imperfect and noisy, so there is no guarantee this assumption is satisfied. Inspired by regression, this paper presents a…
This paper discusses a special kind of convex constrained optimization problem, whose constraints consist of box inequalities and linear equalities. For this problem, in addition to general optimization algorithms such as exact penalty…
The problem of computing minimally sparse solutions of under-determined linear systems is $NP$ hard in general. Subsets with extra properties, may allow efficient algorithms, most notably problems with the restricted isometry property (RIP)…
In many classification problems a classifier should be robust to small variations in the input vector. This is a desired property not only for particular transformations, such as translation and rotation in image classification problems,…
This paper presents a convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems that are non-convex in the input norm, which is a…
These lecture notes summarize various summer schools that I have given on the topic of solving inverse problems (state and parameter estimation) by combining optimally measurement observations and parametrized PDE models. After defining a…
We introduce a new class of convex-regularized Optimal Transport losses, which generalizes the classical Entropy-regularization of Optimal Transport and Sinkhorn divergences, and propose a generalized Sinkhorn algorithm. Our framework…
We consider a weak adversarial network approach to numerically solve a class of inverse problems, including electrical impedance tomography and dynamic electrical impedance tomography problems. We leverage the weak formulation of PDE in the…
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…
A critical decision process in data acquisition for mineral and energy resource exploration is how to efficiently combine a variety of sensor types and to minimize total cost. We propose a probabilistic framework for multi-objective…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In…
When designing a motion planner for autonomous robots there are usually multiple objectives to be considered. However, a cost function that yields the desired trade-off between objectives is not easily obtainable. A common technique across…
This paper considers the problem of minimizing the ordered weighted average (or ordered median) function of finitely many rational functions over compact semi-algebraic sets. Ordered weighted averages of rational functions are not, in…
This paper studies two classes of variational problems introduced in [7], related to the optimal shapes of tree roots and branches. Given a measure $\mu$ describing the distribution of leaves, a sunlight functional $\S(\mu)$ computes the…