We consider adjustable robust linear complementarity problems and extend the results of Biefel et al. (SIAM J Optim 32:152–172, 2022) towards convex and compact uncertainty sets. Moreover, for the case of polyhedral uncertainty sets, we prove that computing an adjustable robust solution of a...

In 1964, Polyak showed that the Heavy-ball method, the simplest momentum technique, accelerates convergence of strongly-convex problems in the vicinity of the solution. While Nesterov later developed a globally accelerated version, Polyak's original algorithm remains simpler and more widely used...

We propose a gradient-based method to solve quasiconvex optimization problems through decomposed optimization and prove local superlinear convergence under mild regularity assumptions at the optimal solution. A practical implementation further provides global convergence while maintaining the...

Bilevel problems are used to model the interaction between two decision makers in which the lower-level problem, the so-called follower's problem, appears as a constraint in the upper-level problem of the so-called leader. One issue in many practical situations is that the follower's problem is...

In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an explicit elementary computation of the so-called second...

In this note, we present an elementary proof for a well-known second-order sufficient optimality condition in nonlinear semidefinite optimization which does not rely on the enhanced theory of second-order tangents. Our approach builds on an explicit elementary computation of the so-called second...

Constrained Bayesian optimization optimizes a black-box objective function subject to black-box constraints. For simplicity, most existing works assume that multiple constraints are independent. To ask, when and how does dependence between constraints help? , we remove this assumption and...

More than three decades ago, Boyd and Balakrishnan established a regularity result for the two-norm of a transfer function at maximizers. Their result extends easily to the statement that the maximum eigenvalue of a univariate real analytic Hermitian matrix family is twice continuously...

We develop a Nash equilibrium problem representing a perfectly competitive market wherein all players are subject to the same source of uncertainty with an unknown probability distribution. Each player—depending on her individual access to and confidence over empirical data—builds an...

We analyze the tail behavior of solutions to sample average approximations (SAAs) of stochastic programs posed in Hilbert spaces. We require that the integrand be strongly convex with the same convexity parameter for each realization. Combined with a standard condition from the literature on...