Related papers: Joint chance-constrained programs and the intersec…
We propose a method to generate cutting-planes from multiple covers of knapsack constraints. The covers may come from different knapsack inequalities if the weights in the inequalities form a totally-ordered set. Thus, we introduce and…
In this paper, we investigate a class of submodular problems which in general are very hard. These include minimizing a submodular cost function under combinatorial constraints, which include cuts, matchings, paths, etc., optimizing a…
We investigate mixed-integer second-order conic (SOC) sets with a nonlinear right-hand side in the SOC constraint, a structure frequently arising in mixed-integer quadratically constrained programming (MIQCP). Under mild assumptions, we…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…
We study the minimization of a rank-one quadratic with indicators and show that the underlying set function obtained by projecting out the continuous variables is supermodular. Although supermodular minimization is, in general, difficult,…
We consider minimization problems with bisubmodular objective functions. We propose valid inequalities, namely the poly-bimatroid inequalities, and provide a complete linear description of the convex hull of the epigraph of a bisubmodular…
In this paper, the compact linearization approach originally proposed for binary quadratic programs with assignment constraints is generalized to such programs with arbitrary linear equations and inequalities that have positive coefficients…
We introduce a novel approach to reduce the computational effort of solving mixed-integer convex chance constrained programs through the scenario approach. Instead of reducing the number of required scenarios, we directly minimize the…
We study the problem of predicting a set or list of options under knapsack constraint. The quality of such lists are evaluated by a submodular reward function that measures both quality and diversity. Similar to DAgger (Ross et al., 2010),…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…
We prove new necessary and sufficient conditions to carry out a compact linearization approach for a general class of binary quadratic problems subject to assignment constraints as it has been proposed by Liberti in 2007. The new conditions…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
With the advent of ubiquitous monitoring and measurement protocols, studies have started to focus more and more on complex, multivariate and heterogeneous datasets. In such studies, multivariate response variables are drawn from a…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satisfied probabilistically. Only the information of the mean and covariance matrix is available, and we solve…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
Understanding how biological constraints shape neural computation is a central goal of computational neuroscience. Spatially embedded recurrent neural networks provide a promising avenue to study how modelled constraints shape the combined…
DR-submodular functions encompass a broad class of functions which are generally non-convex and non-concave. We study the problem of minimizing any DR-submodular function, with continuous and general integer variables, under box constraints…
In this paper, we study chance constrained mixed integer program with consideration of recourse decisions and their incurred cost, developed on a finite discrete scenario set. Through studying a non-traditional bilinear mixed integer…