Related papers: Multiparametric robust solutions for combinatorial…
Gamma uncertainty sets have been introduced for adjusting the degree of conservatism of robust counterparts of (discrete) linear programs. The contribution of this paper is a generalization of this approach to (mixed integer) nonlinear…
This paper presents a novel robust trajectory optimization method for constrained nonlinear dynamical systems subject to unknown bounded disturbances. In particular, we seek optimal control policies that remain robustly feasible with…
We survey results on the hardness of approximating combinatorial optimization problems.
Discrete-time robust optimal control problems generally take a min-max structure over continuous variable spaces, which can be difficult to solve in practice. In this paper, we extend the class of such problems that can be solved through a…
The optimal pricing problem is a fundamental problem that arises in combinatorial auctions. Suppose that there is one seller who has indivisible items and multiple buyers who want to purchase a combination of the items. The seller wants to…
We propose a new methodology for parameterized constrained robust optimization, an important class of optimization problems under uncertainty, based on learning with a self-supervised penalty-based loss function. Whereas supervised learning…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
We consider a suboptimal solution path algorithm for the Support Vector Machine. The solution path algorithm is an effective tool for solving a sequence of a parametrized optimization problems in machine learning. The path of the solutions…
Interdiction problems ask about the worst-case impact of a limited change to an underlying optimization problem. They are a natural way to measure the robustness of a system, or to identify its weakest spots. Interdiction problems have been…
This paper describes a novel approach to planning which takes advantage of decision theory to greatly improve robustness in an uncertain environment. We present an algorithm which computes conditional plans of maximum expected utility. This…
The control and sensing of large-scale systems results in combinatorial problems not only for sensor and actuator placement but also for scheduling or observability/controllability. Such combinatorial constraints in system design and…
In this study we analyze linear mixed-integer programming problems, in which the distribution of the cost vector is only observable through a finite training data set. In contrast to the related studies, we assume that the number of random…
We show how combinatorial optimisation algorithms can be applied to the problem of identifying c-optimal experimental designs when there may be correlation between and within experimental units and evaluate the performance of relevant…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
This paper surveys the recent attempts at leveraging machine learning to solve constrained optimization problems. It focuses on surveying the work on integrating combinatorial solvers and optimization methods with machine learning…
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Structural learning, a method to estimate the parameters for discrete energy minimization, has been proven to be effective in solving computer vision problems, especially in 3D scene parsing. As the complexity of the models increases,…
Robust Optimization has traditionally taken a pessimistic, or worst-case viewpoint of uncertainty which is motivated by a desire to find sets of optimal policies that maintain feasibility under a variety of operating conditions. In this…
This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…