We present a feedback scheme for non-cooperative dynamic games and investigate its stabilizing properties. The dynamic games are modeled as generalized Nash equilibrium problems (GNEP) in which the shared constraint consists of linear time-discrete dynamic equations (e.g., sampled from a partial or ordinary differential equation), which are jointly controlled by the players’ actions. Further, the … Read more
Optimization over the set of matrices \(X\) that satisfy \(X^\top B X = I_p\), referred to as the generalized Stiefel manifold, appears in many applications involving sampled covariance matrices such as the canonical correlation analysis (CCA), independent component analysis (ICA), and the generalized eigenvalue problem (GEVP). Solving these problems is typically done by iterative methods … Read more
The feasibility-seeking approach offers a systematic framework for managing and resolving intricate constraints in continuous problems, making it a promising avenue to explore in the context of floorplanning problems with increasingly heterogeneous constraints. The classic legality constraints can be expressed as the union of convex sets. However, conventional projection-based algorithms for feasibility-seeking do not guarantee … Read more
Chandrasekaran and Shah (2017) used the exponential cone to model the second-order cone in demonstration of its modeling capabilities. We simplify and extend this result to general power cones. ArticleDownload View PDF
Geodesic metric spaces support a variety of averaging constructions for given finite sets. Computing such averages has generated extensive interest in diverse disciplines. Here we consider the inverse problem of recognizing computationally whether or not a given point is such an average, exactly or approximately. In nonpositively curved spaces, several averaging notions, including the usual … Read more
This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the $l$-type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms … Read more
A derivation of so-called “soft-margin support vector machines with kernel” is presented along with elementary proofs that do not rely on concepts from functional analysis such as Mercer’s theorem or reproducing kernel Hilbert spaces which are frequently cited in this context. The analysis leads to new continuity properties of the kernel functions, in particular a … Read more
This work introduces solar, a collection of ten optimization problem instances for benchmarking blackbox optimization solvers. The instances present different design aspects of a concentrated solar power plant simulated by blackbox numerical models. The type of variables (discrete or continuous), dimensionality, and number and types of constraints (including hidden constraints) differ across instances. Some are deterministic, others are stochastic … Read more
We consider solving huge-scale instances of (convex) conic linear optimization problems, at the scale where matrix-factorization-free methods are attractive or necessary. The restarted primal-dual hybrid gradient method (rPDHG) — with heuristic enhancements and GPU implementation — has been very successful in solving huge-scale linear programming (LP) problems; however its application to more general conic convex … Read more
The field of global optimization has advanced significantly over the past three decades. Yet, the solution of even small instances of many nonconvex optimization problems involving the Euclidean norm to global optimality remains beyond the reach of modern global optimization methods. These problems include numerous well-known and high-impact open research questions from a diverse collection … Read more