相关论文: Analytic Center Cutting Plane Methods for Variatio…

We investigate the method of conjugate gradients, exploiting inaccurate matrix-vector products, for the solution of convex quadratic optimization problems. Theoretical performance bounds are derived, and the necessary quantities occurring…

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are…

We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…

We study an abstract setting for cutting planes for integer programming called the infinite group problem. In this abstraction, cutting planes are computed via cut generating function that act on the simplex tableau. In this function space,…

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and…

We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…

Semi-analytical methods, such as rigorous coupled wave analysis, have been pivotal for numerical analysis of photonic structures. In comparison to other methods, they offer much faster computation, especially for structures with constant…

We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…

Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…

In this paper, we propose a cutting plane algorithm based on DC (Difference-of-Convex) programming and DC cut for globally solving Mixed-Binary Linear Program (MBLP). We first use a classical DC programming formulation via the exact…

We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…

A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is…

In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradient-cutting algorithm which is extended from…

In this paper, we present a unified analysis of methods for such a wide class of problems as variational inequalities, which includes minimization problems and saddle point problems. We develop our analysis on the modified Extra-Gradient…

A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…

Current pseudo-Boolean solvers implement different variants of the cutting planes proof system to infer new constraints during conflict analysis. One of these variants is generalized resolution, which allows to infer strong constraints, but…

Gradient descent algorithms perform well in convex optimization but can get tied for finding local minima in non-convex optimization. A robust method that combines a spectral approach with nonmonotone line search strategy for solving…

Motivated by many applications in complex domains with boundaries exposed to large topological changes or deformations, fictitious domain methods regard the actual domain of interest as being embedded in a fixed Cartesian background. This…

Recent advances in the area of plane segmentation from single RGB images show strong accuracy improvements and now allow a reliable segmentation of indoor scenes into planes. Nonetheless, fine-grained details of these segmentation masks are…

A new exact projective penalty method is proposed for the equivalent reduction of constrained optimization problems to nonsmooth unconstrained ones. In the method, the original objective function is extended to infeasible points by summing…