Related papers: The LP-Newton Method and Conic Optimization
Support vector classification (SVC) with logistic loss has excellent theoretical properties in classification problems where the label values are not continuous. In this paper, we reformulate the hyperparameter selection for SVC with…
Mixed-integer nonlinear optimization encompasses a broad class of problems that present both theoretical and computational challenges. We propose a new type of method to solve these problems based on a branch-and-bound algorithm with convex…
We explore computational aspects of maximum likelihood estimation of the mixture proportions of a nonparametric finite mixture model -- a convex optimization problem with old roots in statistics and a key member of the modern data analysis…
Our contribution in this paper is two folded. We consider first the case of linear programming with real coefficients and give a method which allows the computation of a new upper bound on the distance from the origin to a feasible point.…
In this work we develop and analyze a semi-smooth Newton method for the general nonlinear conic programming problem. In particular, we study the problem with a generalized simplicial cone, i.e., the image of a symmetric cone under a linear…
In this paper we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints, are locally smooth. For solving this problem, we propose a…
Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this…
We study the composite convex optimization problems with a Quasi-Self-Concordant smooth component. This problem class naturally interpolates between classic Self-Concordant functions and functions with Lipschitz continuous Hessian.…
We propose a distributed, cubic-regularized Newton method for large-scale convex optimization over networks. The proposed method requires only local computations and communications and is suitable for federated learning applications over…
The problem of minimizing a sum of local convex objective functions over a networked system captures many important applications and has received much attention in the distributed optimization field. Most of existing work focuses on…
This work blends the inexact Newton method with iterative combined approximations (ICA) for solving topology optimization problems under the assumption of geometric nonlinearity. The density-based problem formulation is solved using a…
We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball. Our algorithm replaces the top singular-vector computation ($1$-SVD) in Frank-Wolfe with a top-$k$ singular-vector…
In this paper, we extend and investigate the properties of the semi-smooth Newton method when applied to a general projection equation in finite dimensional spaces. We first present results concerning Clarke's generalized Jacobian of the…
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers…
In this paper the simplicial cone constrained convex quadratic programming problem is studied. The optimality conditions of this problem consist in a linear complementarity problem. This fact, under a suitable condition, leads to an…
Newton-type methods enjoy fast local convergence and strong empirical performance, but achieving global guarantees comparable to first-order methods remains challenging. Even for simple strongly convex problems, no straightforward variant…
We consider a bilevel program involving a linear lower level problem with left-hand-side perturbation. We then consider the Karush-Kuhn-Tucker reformulation of the problem and subsequently build a tractable optimization problem with linear…
This study proposes a cubic regularization of the Newton method for generating weakly efficient points of unconstrained vector optimization problems under no convexity assumption on the objective function. It is observed that at a given…
Discretization of non-linear Poisson-Boltzmann Equation equations results in a system of non-linear equations with symmetric Jacobian. The Newton algorithm is the most useful tool for solving non-linear equations. It consists of solving a…
We consider the NP-hard problem of minimizing a convex quadratic function over the integer lattice ${\bf Z}^n$. We present a simple semidefinite programming (SDP) relaxation for obtaining a nontrivial lower bound on the optimal value of the…