Related papers: Unique End of Potential Line
Partially-observable Markov decision processes (POMDPs) with discounted-sum payoff are a standard framework to model a wide range of problems related to decision making under uncertainty. Traditionally, the goal has been to obtain policies…
We present a new convex method to estimate 3D pose from mixed combinations of 2D-3D point and line correspondences, the Perspective-n-Points-and-Lines problem (PnPL). We merge the contributions of each point and line into a unified…
The promise constraint satisfaction problem (PCSP) is a recently introduced vast generalisation of the constraint satisfaction problem (CSP) that captures approximability of satisfiable instances. A PCSP instance comes with two forms of…
Penalty methods are a well known class of algorithms for constrained optimization. They transform a constrained problem into a sequence of unconstrained \emph{penalized} problems in the hope that approximate solutions of the latter converge…
We develop a unified framework to characterize the power of higher-level algorithms for the constraint satisfaction problem (CSP), such as $k$-consistency, the Sherali-Adams LP hierarchy, and the affine IP hierarchy. As a result,…
We show how two techniques from statistical physics can be adapted to solve a variant of the notorious Unique Games problem, potentially opening new avenues towards the Unique Games Conjecture. The variant, which we call Count Unique Games,…
Multi-task learning (MTL), which aims to improve performance by learning multiple tasks simultaneously, inherently presents an optimization challenge due to multiple objectives. Hence, multi-objective optimization (MOO) approaches have been…
Among the hardest tasks for humans are those found in competitive programming where problems require sophisticated algorithmic thinking, puzzle solving, and the creation of effective code. As a domain to assess language models (LMs), it has…
We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought;…
While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology. The gradients from the PDE residuals and boundary constraints oppose…
In the field of constraint satisfaction problems (CSP), promise CSPs are an exciting new direction of study. In a promise CSP, each constraint comes in two forms: "strict" and "weak," and in the associated decision problem one must…
This paper studies the computational complexity of the Edge Packing problem and the Vertex Packing problem. The edge packing problem (denoted by $\bar{EDS}$) and the vertex packing problem (denoted by $\bar{DS} $) are linear programming…
Power systems Unit Commitment (UC) problem determines the generator commitment schedule and dispatch decisions to realize the reliable and economic operation of power networks. The growing penetration of stochastic renewables and demand…
Unique-sink orientations (USOs) are an abstract class of orientations of the n-cube graph. We consider some classes of USOs that are of interest in connection with the linear complementarity problem. We summarise old and show new lower and…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operations research, and optimization. Despite the consistent efforts on this problem, all…
The optimization problems associated with training generative adversarial neural networks can be largely reduced to certain {\em non-monotone} variational inequality problems (VIPs), whereas existing convergence results are mostly based on…
When dealing with real-world optimization problems, decision-makers usually face high levels of uncertainty associated with partial information, unknown parameters, or complex relationships between these and the problem decision variables.…
Error bounds, which refer to inequalities that bound the distance of vectors in a test set to a given set by a residual function, have proven to be extremely useful in analyzing the convergence rates of a host of iterative methods for…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…