We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has ...

An abstract optimization problem of minimizing a functional on a convex subset of a Banach space is considered. We discuss natural assumptions on the functional that permit establishing sufficient second-order optimality conditions with minimal gap with ...

Existence, uniqueness, and approximations of smooth solutions to team optimization problems with stochastic information structure are investigated. Suboptimal strategies made up of linear combinations of basis functions containing adjustable parameters ...

In this paper, a method for solving constrained convex optimization problems is introduced. The problem is cast equivalently as a parametric unconstrained one, the (single) parameter being the optimal value of the original problem. At each stage of the ...

We propose an interior-point algorithm based on an elastic formulation of the $\ell_1$-penalty merit function for mathematical programs with complementarity constraints. The salient feature of our method is that it requires no prior knowledge of which ...

We discuss minimization of a smooth function to which is added a separable regularization function that induces structure in the solution. A block-coordinate relaxation approach with proximal linearized subproblems yields convergence to critical points, ...

In this paper we propose an efficient method for solving the spherically constrained homogeneous polynomial optimization problem. The new approach has the following three main ingredients. First, we establish a block coordinate descent type search ...

We describe multistage stochastic programs in a purely in-distribution setting, i.e., without any reference to a concrete probability space. The concept is based on the notion of nested distributions, which encompass in one mathematical object the ...

The (optimal) function/gradient evaluations worst-case complexity analysis available for the adaptive regularization algorithms with cubics (ARC) for nonconvex smooth unconstrained optimization is extended to finite-difference versions of this algorithm,...

We consider the problem of locating a user's position from a set of noisy pseudoranges to a group of satellites. We consider both the nonlinear least squares formulation of the problem, which is nonconvex and nonsmooth, and the nonlinear squared least ...

The stability of error bounds is significant in optimization theory and applications. Based on either the linearity assumption or the convexity and finite dimension assumption, several authors have focused on perturbation analysis of error bounds and ...

For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson's constraint qualification, we show that the nonsingularity of Clarke's Jacobian of the Fischer-Burmeister (FB) nonsmooth system is equivalent to the strong ...

We estimate the worst-case complexity of minimizing an unconstrained, nonconvex composite objective with a structured nonsmooth term by means of some first-order methods. We find that it is unaffected by the nonsmoothness of the objective in that a ...

We present a bundle method for convex nondifferentiable minimization where the model is a piecewise-quadratic convex approximation of the objective function. Unlike standard bundle approaches, the model only needs to support the objective function from ...

This paper develops an optimization-based theory for the existence and uniqueness of equilibria of a noncooperative game wherein the selfish players' optimization problems are nonconvex and there are side constraints and an associated price clearance to ...

Mathematical programs in which the constraint set is partially defined by the solutions of an elliptic variational inequality, so-called “elliptic MPECs,” are formulated in reflexive Banach spaces. With the goal of deriving explicit first-order ...

In this paper, we consider both a variant of Tseng's modified forward-backward splitting method and an extension of Korpelevich's method for solving hemivariational inequalities with Lipschitz continuous operators. By showing that these methods are ...

To find a global optimal solution to the quadratically constrained quadratic programming problem, we explore the relationship between its Lagrangian multipliers and related linear conic programming problems. This study leads to a global optimality ...

We compare six state-of-the-art local optimization solvers, with a focus on their efficiency when invoked within an interval-based global optimization algorithm. For comparison purposes we design three special performance indicators: a solution check ...

This is the first paper dealing with the study of weak sharp minima for constrained optimization problems on Riemannian manifolds, which are important in many applications. We consider the notions of local weak sharp minima, boundedly weak sharp minima, ...