Related papers: Log-domain interior-point methods for convex quadr…

We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…

We propose an inexact infeasible arc-search interior-point method for solving linear optimization problems. The method combines an arc-search strategy with inexact solutions to Newton systems and admits a polynomial iteration complexity…

In this paper, we study the convergence of an interior subgradient and proximal methods for a DC (difference of convex functions) constrained minimization problem.

Estimation of nonlinear dynamic models from data poses many challenges, including model instability and non-convexity of long-term simulation fidelity. Recently Lagrangian relaxation has been proposed as a method to approximate simulation…

We develop a new `subspace layered least squares' interior point method (IPM) for solving linear programs. Applied to an $n$-variable linear program in standard form, the iteration complexity of our IPM is up to an $O(n^{1.5} \log n)$…

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain…

In a recent paper, Skajaa and Ye proposed a homogeneous primal-dual interior-point method for non-symmetric conic optimization. The authors showed that their algorithm converges to $\varepsilon$-accuracy in $O(\sqrt{\nu}\log…

We present a coordinate ascent method for a class of semidefinite programming problems that arise in non-convex quadratic integer optimization. These semidefinite programs are characterized by a small total number of active constraints and…

This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem…

When an inverse problem is solved by a gradient-based optimization algorithm, the corresponding forward and adjoint problems, which are introduced to compute the gradient, can be also solved iteratively. The idea of iterating at the same…

We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…

This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…

In pure integer linear programming it is often desirable to work with polyhedra that are full-dimensional, and it is well known that it is possible to reduce any polyhedron to a full-dimensional one in polynomial time. More precisely, using…

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 perform a smoothed analysis of the termination phase of an interior-point method. By combining this analysis with the smoothed analysis of Renegar's interior-point algorithm by Dunagan, Spielman and Teng, we show that the smoothed…

This note discusses an essentially decentralized interior point method, which is well suited for optimization problems arising in energy networks. Advantages of the proposed method are guaranteed and fast local convergence also for problems…

In linear optimization, matrix structure can often be exploited algorithmically. However, beneficial presolving reductions sometimes destroy the special structure of a given problem. In this article, we discuss structure-aware…

In this paper we consider constrained optimization problems where both the objective and constraint functions are of the black-box type. Furthermore, we assume that the nonlinear inequality constraints are non-relaxable, i.e. their values…

Numerous interesting properties in nonlinear systems analysis can be written as polynomial optimization problems with nonconvex sum-of-squares problems. To solve those problems efficiently, we propose a sequential approach of local…

Let $F \in \R[X_1,\ldots,X_n]$ and the zero set $V=\zero(\mathcal{P},\R^n)$, where $\mathcal{P}:=\{P_1,\ldots,P_s\} \subset \R[X_1,\ldots,X_n]$ is a finite set of polynomials. We investigate existence of critical points of $F$ on an…