Related papers: ALSO-X and ALSO-X+: Better Convex Approximations f…
We develop two new proximal alternating penalty algorithms to solve a wide range class of constrained convex optimization problems. Our approach mainly relies on a novel combination of the classical quadratic penalty, alternating…
We consider Constrained Online Convex Optimization (COCO) with adversarially chosen constraints. At each round, the learner chooses an action before observing the loss and constraint function for that round. The goal is to achieve small…
We propose conformal predictive programming (CPP), a framework to solve chance constrained optimization problems, i.e., optimization problems with constraints that are functions of random variables. CPP utilizes samples from these random…
This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an…
In the Correlation Clustering problem we are given $n$ nodes, and a preference for each pair of nodes indicating whether we prefer the two endpoints to be in the same cluster or not. The output is a clustering inducing the minimum number of…
We consider potentially non-convex optimization problems, for which optimal rates of approximation depend on the dimension of the parameter space and the smoothness of the function to be optimized. In this paper, we propose an algorithm…
We propose a novel approximation hierarchy for cardinality-constrained, convex quadratic programs that exploits the rank-dominating eigenvectors of the quadratic matrix. Each level of approximation admits a min-max characterization whose…
In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing…
Constraint Programming (CP) solvers typically tackle optimization problems by repeatedly finding solutions to a problem while placing tighter and tighter bounds on the solution cost. This approach is somewhat naive, especially for…
This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal…
We give an attribution method for neural combinatorial-optimisation (CO) policies that (i) decomposes a decision by constraint families via LP-relaxation duals, (ii) certifies counterfactuals through a combinatorial feasibility model…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
We propose an iterative gradient-based algorithm to efficiently solve the portfolio selection problem with multiple spectral risk constraints. Since the conditional value at risk (CVaR) is a special case of the spectral risk measure, our…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
We propose new sequential simulation-optimization algorithms for general convex optimization via simulation problems with high-dimensional discrete decision space. The performance of each choice of discrete decision variables is evaluated…
This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general…
In model predictive control (MPC) an optimization problem has to be solved at each time step, which in real-time applications makes it important to solve these optimization problems efficiently and to have good upper bounds on worst-case…
The addition of lower level integrality constraints to a bi-level linear program is known to result in significantly weaker analytical properties. Most notably, the upper level goal function in the optimistic setting lacks lower…
In many operational settings, decision-makers must commit to actions before uncertainty resolves, but existing optimization tools rarely quantify how consistently a chosen decision remains optimal across plausible scenarios. This paper…