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With the help of Generalized Estimating Equations, we identify locally D-optimal crossover designs for generalized linear models. We adopt the variance of parameters of interest as the objective function, which is minimized using…

Devising efficient algorithms that track the optimizers of continuously varying convex optimization problems is key in many applications. A possible strategy is to sample the time-varying problem at constant rate and solve the resulting…

We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…

The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…

In this paper we study two classes of imprecise previsions, which we termed convex and centered convex previsions, in the framework of Walley's theory of imprecise previsions. We show that convex previsions are related with a concept of…

In this paper, we propose a general algorithmic framework for first-order methods in optimization in a broad sense, including minimization problems, saddle-point problems, and variational inequalities. This framework allows obtaining many…

The presence of second-order smoothness for objective functions of optimization problems can provide valuable information about their stability properties and help us design efficient numerical algorithms for solving these problems. Such…

This paper is devoted to developing and applications of a generalized differential theory of variational analysis that allows us to work in incomplete normed spaces, without employing conventional variational techniques based on…

In the article we discuss the notion of the generalized invariant manifold introduced in our previous study. In the literature the method of the differential constraints is well known as a tool for constructing particular solutions for the…

In this paper we established new integral inequalities which are more general results for coordinated convex functions on the coordinates by using some classical inequalities.

Submodularity is one of the most well-studied properties of problem classes in combinatorial optimization and many applications of machine learning and data mining, with strong implications for guaranteed optimization. In this thesis, we…

A complete classification of continuous, dually epi-translation invariant, and rotation equivariant valuations on convex functions is established. This characterizes the recently introduced functional Minkowski vectors, which naturally…

We extend the notion of anti-unification to cover equational theories and present a method based on regular tree grammars to compute a finite representation of E-generalization sets. We present a framework to combine Inductive Logic…

Motivated by recent increased interest in optimization algorithms for non-convex optimization in application to training deep neural networks and other optimization problems in data analysis, we give an overview of recent theoretical…

We show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas: the separation principle of convex analysis, and integral representations of continuous…

In this article we utilise abstract convexity theory in order to unify and generalize many different concepts from nonsmooth analysis. We introduce the concepts of abstract codifferentiability, abstract quasidifferentiability and abstract…

We present Epsilon, a system for general convex programming using fast linear and proximal operators. As with existing convex programming frameworks, users specify convex optimization problems using a natural grammar for mathematical…

In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different…

Quality statistical inference requires a sufficient amount of data, which can be missing or hard to obtain. To this end, prediction-powered inference has risen as a promising methodology, but existing approaches are largely limited to…

Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…