Related papers: First- and second-order optimality conditions for …
We give the most general conditions to date which lead to uniqueness of the general relativistic Hamiltonian. Namely, we show that all spatially covariant generalizations of the scalar constraint which extend the standard one while…
Necessary conditions for high-order optimality in smooth nonlinear constrained optimization are explored and their inherent intricacy discussed. A two-phase minimization algorithm is proposed which can achieve approximate first-, second-…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
This is a review paper, summarizing without proofs recent results by the authors on the property of strong metric subregularity (SMSR) in optimization. It presents sufficient conditions for SMSR of the optimality mapping associated with a…
Optimization problems with rank constraints appear in many diverse fields such as control, machine learning and image analysis. Since the rank constraint is non-convex, these problems are often approximately solved via convex relaxations.…
We provide a generalization of first-order necessary conditions of optimality for infinite-dimensional optimization problems with a finite number of inequality constraints and with a finite number of inequality and equality constraints. Our…
Optimization problems involving minimization of a rank-one convex function over constraints modeling restrictions on the support of the decision variables emerge in various machine learning applications. These problems are often modeled…
This paper investigates the optimality conditions for characterizing the local minimizers of the constrained optimization problems involving an $\ell_p$ norm ($0<p<1$) of the variables, which may appear in either the objective or the…
This paper considers mathematical programs, whose constraints are expressed by a parameterized vector equilibrium problem. The latter is a well recognized framework, which is able to cover multicriteria optimization, vector variational…
We consider the Moment-SOS hierarchy in polynomial optimization. We first provide a sufficient condition to solve the truncated K-moment problem associated with a given degree-$2n$ pseudo-moment sequence $\phi$ n and a semi-algebraic set $K…
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a…
We develop a principled approach to obtain exact computer-aided worst-case guarantees on the performance of second-order optimization methods on classes of univariate functions. We first present a generic technique to derive interpolation…
In this paper, "chance optimization" problems are introduced, where one aims at maximizing the probability of a set defined by polynomial inequalities. These problems are, in general, nonconvex and computationally hard. With the objective…
We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…
We present an analysis of sets of matrices with rank less than or equal to a specified number $s$. We provide a simple formula for the normal cone to such sets, and use this to show that these sets are prox-regular at all points with rank…
We study a class of two-stage stochastic programs in which the second stage includes a set of components with uncertain capacity, and the expression for the distribution function of the uncertain capacity includes first-stage variables.…
Linear convergence of first-order methods is typically characterized by global optimization conditions whose constants reflect worst-case geometry of the ambient space. In high-dimensional or structured problems, these global constants can…
We propose a new homotopy-based conditional gradient method for solving convex optimization problems with a large number of simple conic constraints. Instances of this template naturally appear in semidefinite programming problems arising…
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…
Qualification has been recently introduced as a generalization of uncertainty in the field of Logic Programming. In this report we investigate a more expressive language for First-Order Functional Logic Programming with Constraints and…