Related papers: Constraint Qualifications and Optimality Condition…
In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions objects are…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
We present a focused introduction to exact penalty methods for nonlinear programs and mathematical programs with equilibrium constraints (MPECs), emphasizing their connection to modern error bound theory. The goal is twofold. First, we…
The paper addresses parametric inequality systems described by polynomial functions in finite dimensions, where state-dependent infinite parameter sets are given by finitely many polynomial inequalities and equalities. Such systems can be…
We present and analyze a central cutting surface algorithm for general semi-infinite convex optimization problems, and use it to develop a novel algorithm for distributionally robust optimization problems in which the uncertainty set…
In this work, we consider a class of convex optimization problems in a real Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those…
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…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
We establish necessary conditions of optimality for discrete-time infinite-horizon optimal control in presence of constraints at infinity. These necessary conditions are in form of weak and strong Pontryagin principles. We use a functional…
We study fundamental limits of first-order stochastic optimization in a range of nonconvex settings, including L-smooth functions satisfying Quasar-Convexity (QC), Quadratic Growth (QG), and Restricted Secant Inequalities (RSI). While the…
The scenario-based optimization approach (`scenario approach') provides an intuitive way of approximating the solution to chance-constrained optimization programs, based on finding the optimal solution under a finite number of sampled…
Developing classification algorithms that are fair with respect to sensitive attributes of the data has become an important problem due to the growing deployment of classification algorithms in various social contexts. Several recent works…
We describe a factor-revealing convex optimization problem for the integrality gap of the maximum-cut semidefinite programming relaxation: for each $n \geq 2$ we present a convex optimization problem whose optimal value is the largest…
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…
We study optimization programs given by a bilinear form over non-commutative variables subject to linear inequalities. Problems of this form include the entangled value of two-prover games, entanglement-assisted coding for classical…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…
We study one-dimensional integral inequalities, with quadratic integrands, on bounded domains. Conditions for these inequalities to hold are formulated in terms of function matrix inequalities which must hold in the domain of integration.…
We discuss a weak constraint qualification for conic linear programs and its applications for a few classes of cones. This constraint qualification is used to give a solution to a problem proposed by Shapiro and Z\v{a}linescu and show that…
The constant rank constraint qualification, introduced by Janin in 1984 for nonlinear programming, has been extensively used for sensitivity analysis, global convergence of first- and second-order algorithms, and for computing the…
We propose a general method for optimization with semi-infinite constraints that involve a linear combination of functions, focusing on the case of the exponential function. Each function is lower and upper bounded on sub-intervals by…