Related papers: Variational Analysis of Composite Models with Appl…

This paper presents an optimization approach for generating custom manipulator configurations using a proposed unconventional modular library. An end-to-end solution is presented in which the resulting optimal models of the modular…

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

Dimension reduction for high-dimensional compositional data plays an important role in many fields, where the principal component analysis of the basis covariance matrix is of scientific interest. In practice, however, the basis variables…

Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…

A new method of deriving comparative statics information using generalized compensated derivatives is presented which yields constraint-free semidefiniteness results for any differentiable, constrained optimization problem. More generally,…

We analyze combinatorial optimization problems with ordinal, i.e., non-additive, objective functions that assign categories (like good, medium and bad) rather than cost coefficients to the elements of feasible solutions. We review different…

We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…

This paper investigates a well-posedness property of parametric constraint systems named here Robinson stability. Based on advanced tools of variational analysis and generalized differentiation, we derive first-order and second-order…

Paradoxically, while the assumptions of second-order stationarity and isotropy appear outdated in light of modern spatial data, they remain remarkably robust in practice, as nonstationary methods often provide marginal improvements in…

We introduce a new compositional framework for generalized variational inference, clarifying the different parts of a model, how they interact, and how they compose. We explain that both exact Bayesian inference and the loss functions…

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and the dual variables. First, we consider such problems with smooth composite…

This paper suggests two novel ideas to develop new proximal variable-metric methods for solving a class of composite convex optimization problems. The first idea is a new parameterization of the optimality condition which allows us to…

The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…

Compositional generalization-a key open challenge in modern machine learning-requires models to predict unknown combinations of known concepts. However, assessing compositional generalization remains a fundamental challenge due to the lack…

In this paper we survey the primary research, both theoretical and applied, in the area of Robust Optimization (RO). Our focus is on the computational attractiveness of RO approaches, as well as the modeling power and broad applicability of…

The optimal value function is one of the basic objects in the field of mathematical optimization, as it allows the evaluation of the variations in the cost/revenue generated while minimizing/maximizing a given function under some…

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…

We present a class of nonconforming virtual element methods for general fourth order partial differential equations in two dimensions. We develop a generic approach for constructing the necessary projection operators and virtual element…

Explicitly accounting for uncertainties is paramount to the safety of engineering structures. Optimization which is often carried out at the early stage of the structural design offers an ideal framework for this task. When the…

We formulate symmetric versions of classical variational principles. Within the framework of non-smooth critical point theory, we detect Palais-Smale sequences with additional second order and symmetry information. We discuss applications…