Related papers: Between steps: Intermediate relaxations between bi…

Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale…

An effective strategy for accelerating the calculation of convex hulls for point sets is to filter the input points by discarding interior points. In this paper, we present such a straightforward and efficient preprocessing approach by…

In the past decade, we had developed a series of splitting contraction algorithms for separable convex optimization problems, at the root of the alternating direction method of multipliers. Convergence of these algorithms was studied under…

Let T be the unit circle in the complex plane C. This paper proves the existence of analytic structure in a compact subset K of T X C^n, where K has so-called "lineally convex" or "hypoconvex" fibers over T. It also addresses a related…

In this paper, we study the convex quadratic optimization problem with indicator variables. For the bivariate case, we describe the convex hull of the epigraph in the original space of variables, and also give a conic quadratic extended…

We show {\it semidefinite programming} (SDP) feasibility problem is equivalent to solving a {\it convex hull relaxation} (CHR) for a finite system of quadratic equations. On the one hand, this offers a simple description of SDP. On the…

We propose a proximal approach to deal with a class of convex variational problems involving nonlinear constraints. A large family of constraints, proven to be effective in the solution of inverse problems, can be expressed as the lower…

The properties of the interface in a phase-separated solution of polymers with different degrees of polymerization and Kuhn segment lengths are calculated. The starting point is the planar interface, the profile of which is calculated in…

We present a new model for hybrid planarity that relaxes existing hybrid representations. A graph $G = (V,E)$ is $(k,p)$-planar if $V$ can be partitioned into clusters of size at most $k$ such that $G$ admits a drawing where: (i) each…

In finite-volume-based flow-simulations with free-surface waves, wave reflections at the domain boundaries can cause substantial errors in the results and must therefore be minimized. This can be achieved via `implicit relaxation zones',…

There are many examples of optimization problems whose associated polyhedra can be described much nicer, and with way less inequalities, by projections of higher dimensional polyhedra than this would be possible in the original space.…

For a complexity class $C$ and language $L$, a constructive separation of $L \notin C$ gives an efficient algorithm (also called a refuter) to find counterexamples (bad inputs) for every $C$-algorithm attempting to decide $L$. We study the…

Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…

When given a generalized matrix separation problem, which aims to recover a low rank matrix $L_0$ and a sparse matrix $S_0$ from $M_0=L_0+HS_0$, the work \cite{CW25} proposes a novel convex optimization problem whose objective function is…

We develop a projection-based decomposition to disentangle structural breaks in the factor variance and factor loadings. Our approach yields test statistics that can be compared against standard distributions commonly used in the structural…

We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…

This paper presents Diff-Explainer, the first hybrid framework for explainable multi-hop inference that integrates explicit constraints with neural architectures through differentiable convex optimization. Specifically, Diff-Explainer…

Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…

This article presents a class of new relaxation modulus-based iterative methods to process the large and sparse implicit complementarity problem (ICP). Using two positive diagonal matrices, we formulate a fixed-point equation and prove that…

A model is constructed in which pair potentials are combined with the cluster expansion method in order to better describe the energetics of structurally relaxed substitutional alloys. The effect of structural relaxations away from the…