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Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…
The puncturing and shortening technique are two important approaches to constructing new linear codes from old ones. In the past 70 years, a lot of progress on the puncturing technique has been made, and many works on punctured linear codes…
Given a set P of n points in the plane, the two-line center problem asks to find two lines that minimize the maximum distance from each point in P to its closer one of the two resulting lines. The currently best algorithm for the problem…
Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
A high-level description of an algorithm which computes the minimum perimeter triangle enclosing a convex polygon in linear time exists in the literature. Besides that an implementation of the algorithm is given in the subsequent work.…
The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their…
We consider the following geometric optimization problem: find a convex polygon of maximum area contained in a given simple polygon $P$ with $n$ vertices. We give a randomized near-linear-time $(1-\varepsilon)$-approximation algorithm for…
Globally non-positively curved, or CAT(0), polyhedral complexes arise in a number of applications, including evolutionary biology and robotics. These spaces have unique shortest paths and are composed of Euclidean polyhedra, yet many…
A common representation of a three dimensional object in computer applications, such as graphics and design, is in the form of a triangular mesh. In many instances, individual or groups of triangles in such representation need to satisfy…
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Riemannian optimization algorithms, which minimize the…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
The existing convolutional neural network pruning algorithms can be divided into two categories: coarse-grained clipping and fine-grained clipping. This paper proposes a coarse and fine-grained automatic pruning algorithm, which can achieve…
Given a rectangle $R$ with area $A$ and a set of areas $L=\{A_1,...,A_n\}$ with $\sum_{i=1}^n A_i = A$, we consider the problem of partitioning $R$ into $n$ sub-regions $R_1,...,R_n$ with areas $A_1,...,A_n$ in a way that the total…
In this paper, we present a novel nonlinear programming-based approach to fine-tune pre-trained neural networks to improve robustness against adversarial attacks while maintaining high accuracy on clean data. Our method introduces…
Given a convex polyhedron $P$ of $n$ vertices inside a sphere $Q$, we give an $O(n^3)$-time algorithm that cuts $P$ out of $Q$ by using guillotine cuts and has cutting cost $O((\log n)^2)$ times the optimal.
An ill-posed problem of synthesis of the Pierce electrodes for a cylindrical beam with a polygonal cross-section is considered. It is assumed that a beam of charged particles is extracted from a space-charge-limited planar diode and the…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
While well-known methods to list the intersections of either a list of segments or a complex polygon aim at achieving optimal time-complexity they often do so at the cost of memory comsumption and complex code. Real-life software…