Related papers: On The Projection Operator to A Three-view Cardina…

Learning visual similarity requires to learn relations, typically between triplets of images. Albeit triplet approaches being powerful, their computational complexity mostly limits training to only a subset of all possible training…

Enforcing complex (e.g., nonconvex) operational constraints is a critical challenge in real-world learning and control systems. However, existing methods struggle to efficiently enforce general classes of constraints. To address this, we…

The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…

Boolean cardinality constraints state that at most (at least, or exactly) $k$ out of $n$ propositional literals can be true. We propose a new class of selection networks that can be used for an efficient encoding of them. Several comparator…

This paper considers a conceptual version of a convex optimization algorithm whic is based on replacing a convex optimization problem with the root-finding problem for the approximate sub-differential mapping which is solved by repeated…

The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between…

Wide-field optical imaging surveys are efficient at identifying galaxy clusters, but optically identified clusters suffer from projection effects--physically unassociated galaxies along the line of sight can be misidentified as cluster…

In this article, we derive an iterative scheme through a quasi-Newton technique to capture robust weakly efficient points of uncertain multiobjective optimization problems under the upper set less relation. It is assumed that the set of…

The cardinality constrained optimization problem (CCOP) is an optimization problem where the maximum number of nonzero components of any feasible point is bounded. In this paper, we consider CCOP as a mathematical program with disjunctive…

Galaxy clusters identified with optical imaging tend to suffer from projection effects, which impact richness (the number of member galaxies in a cluster) and lensing coherently. Physically unassociated galaxies can be mistaken as cluster…

We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the…

Recently dictionary screening has been proposed as an effective way to improve the computational efficiency of solving the lasso problem, which is one of the most commonly used method for learning sparse representations. To address today's…

Constraint programming (CP) is a powerful technique for solving constraint satisfaction and optimization problems. In CP solvers, the variable ordering strategy used to select which variable to explore first in the solving process has a…

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. To…

We prove global convergence of classical projection algorithms for feasibility problems involving union convex sets, which refer to sets expressible as the union of a finite number of closed convex sets. We present a unified strategy for…

The minimisation problem of a sum of unary and pairwise functions of discrete variables is a general NP-hard problem with wide applications such as computing MAP configurations in Markov Random Fields (MRF), minimising Gibbs energy, or…

The paper concerns optimization problems with general equality and inequality constraints and with constraints expressed by a convex set. In order to solve these problems, the general constraints are treated by an exact penalty functions…

A distributed nonsmooth robust resource allocation problem with cardinality constrained uncertainty is investigated in this paper. The global objective is consisted of local objectives, which are convex but nonsmooth. Each agent is…

We study the complexity of constraint satisfaction problems involving global constraints, i.e., special-purpose constraints provided by a solver and represented implicitly by a parametrised algorithm. Such constraints are widely used;…