相关论文: No self-concordant barrier interior point method i…

We present an efficient framework for solving algebraically-constrained global non-convex polynomial optimization problems over subsets of the hypercube. We prove the existence of an equivalent nonlinear reformulation of such problems that…

A novel inner approximation algorithm is proposed for dynamic optimization problems to ensure strict satisfaction of path constraints. Distinct from traditional methods relying on interval analysis, the proposed algorithm leverages the…

We study a class of monotone inclusions called "self-concordant inclusion" which covers three fundamental convex optimization formulations as special cases. We develop a new generalized Newton-type framework to solve this inclusion. Our…

We show that the effects of finite-precision arithmetic in forming and solving the linear system that arises at each iteration of primal-dual interior-point algorithms for nonlinear programming are benign, provided that the iterates satisfy…

In this paper, we address an extension of the theory of self-concordant functions for a manifold. We formulate the self-concordance of a geodesically convex function by a condition of the covariant derivative of its Hessian, and verify that…

The motivation for this paper is to study the complexity of constant-width arithmetic circuits. Our main results are the following. 1. For every k > 1, we provide an explicit polynomial that can be computed by a linear-sized monotone…

We give a self-contained proof of the strongest version of Mason's conjecture, namely that for any matroid the sequence of the number of independent sets of given sizes is ultra log-concave. To do this, we introduce a class of polynomials,…

Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…

This work studies the problem of maximizing a higher degree real homogeneous multivariate polynomial over the unit sphere. This problem is equivalent to finding the leading eigenvalue of the associated symmetric tensor of higher order,…

We are interested in finding a nonlinear polynomial $P$ on $\mathbb{R}^n$ that solves the minimal surface equation. Even though no explicit solution is found in this article, we investigate constraints that a polynomial solution must obey.…

We provide an interior point method based on quasi-Newton iterations, which only requires first-order access to a strongly self-concordant barrier function. To achieve this, we extend the techniques of Dunagan-Harvey [STOC '07] to maintain…

Enumeration problems are often encountered as key subroutines in the exact computation of graph parameters such as chromatic number, treewidth, or treedepth. In the case of treedepth computation, the enumeration of inclusion-wise minimal…

We consider minimizing a conic quadratic objective over a polyhedron. Such problems arise in parametric value-at-risk minimization, portfolio optimization, and robust optimization with ellipsoidal objective uncertainty; and they can be…

We use the concept of barrier-based smoothing approximations introduced in [ C. B. Chua and Z. Li, A barrier-based smoothing proximal point algorithm for NCPs over closed convex cones, SIOPT 23(2), 2010] to extend the non-interior…

We consider minimization problems with structured objective function and smooth constraints, and present a flexible framework that combines the beneficial regularization effects of (exact) penalty and interior-point methods. In the fully…

We consider convex programming problems with integrality constraints that are invariant under a linear symmetry group. To decompose such problems we introduce the new concept of core points, i.e., integral points whose orbit polytopes are…

We study the question of whether parallelization in the exploration of the feasible set can be used to speed up convex optimization, in the local oracle model of computation. We show that the answer is negative for both deterministic and…

Arithmetic complexity is considered simpler to understand than Boolean complexity, namely computing Boolean functions via logical gates. And indeed, we seem to have significantly more lower bound techniques and results in arithmetic…

Exploiting tools from algebraic geometry, the problem of finiteness of determination of accessibility/strong accessibility is investigated for polynomial systems and also for analytic systems that are immersible into polynomial systems. The…

We formalize a framework of algebraically natural lower bounds for algebraic circuits. Just as with the natural proofs notion of Razborov and Rudich for boolean circuit lower bounds, our notion of algebraically natural lower bounds captures…