The maximum-entropy sampling problem (MESP) aims to select the most informative principal submatrix of a prespecified size from a given covariance matrix. This paper proposes an augmented factorization bound for MESP based on concave relaxation. By leveraging majorization and Schur-concavity theory, we demonstrate that this new bound dominates the classic factorization bound of Nikolov (2015) and a recent … Read more
\(\) In this paper, we study a class of deterministically constrained stochastic optimization problems. Existing methods typically aim to find an \(\epsilon\)-stochastic stationary point, where the expected violations of both constraints and first-order stationarity are within a prescribed accuracy \(\epsilon\). However, in many practical applications, it is crucial that the constraints be nearly satisfied with … Read more
\(\) We present randomized reconstruction approaches for optimal solutions to mixed-integer elliptic PDE control systems. Approximation properties and relations to sum-up rounding are derived using the cut norm. This enables us to dispose of space-filling curves required for sum-up rounding. Rates of almost sure convergence in the cut norm and the SUR norm in control … Read more
This work deals with convergence to points satisfying the weak second-order necessary optimality conditions of a second-order safeguarded augmented Lagrangian method from the literature. To this end, we propose a new second-order sequential optimality condition that is, in a certain way, based on the iterates generated by the algorithm itself. This also allows us to … Read more
Mathematical modeling, simulation, and optimization can significantly support the development and characterization of chromatography steps in the biopharmaceutical industry. Particularly mechanistic models become preferably used, as these models, once carefully calibrated, can be employed for a reliable optimization. However, model calibration is a difficult task in this context due to high correlations between parameters, highly … Read more
Considering a standard nonlinear programming problem, one may view a subset of the equality constraints as an embedded Riemannian manifold. In this paper we investigate the differences between the Euclidean and the Riemannian approach for this problem. It is well known that the linear independence constraint qualification for both approaches are equivalent. However, when considering … Read more
It is known that second-order (Studniarski) contingent derivatives can be used to compute tangents to the solution set of a generalized equation when standard (first-order) regularity conditions are absent, but relaxed (second-order) regularity conditions are fulfilled. This fact, roughly speaking, is only relevant in practice as long as the computation of second-order contingent derivatives itself … Read more
We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of four algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss-army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with … Read more
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called “l0 norm”, which counts the number of non-zero components in a vector, is a strong reliable mechanism of enforcing … Read more
We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the component of the step corrupted by the variance of the stochastic gradient estimates and a second which scales the entire step. We prove that this … Read more