Related papers: Surface Movement Method for Linear Programming
Segmentation of multiple surfaces in medical images is a challenging problem, further complicated by the frequent presence of weak boundary and mutual influence between adjacent objects. The traditional graph-based optimal surface…
Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…
This paper presents a novel methodology for solving the time-optimal trajectory optimization problem for interplanetary solar-sail missions using successive convex programming. Based on the non-convex problem, different convexification…
Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all…
We describe an approximate dynamic programming approach to compute lower bounds on the optimal value function for a discrete time, continuous space, infinite horizon setting. The approach iteratively constructs a family of lower bounding…
In this paper, we apply the random walk model in designing a raindrop algorithm to find the global optimal solution of a non-linear programming problem. The raindrop algorithm does not require the information of the first or second order…
A numerical method is developed to solve linear semi-infinite programming problem (LSIP) in which the iterates produced by the algorithm are feasible for the original problem. This is achieved by constructing a sequence of standard linear…
In this paper, we propose a low-rank coordinate descent approach to structured semidefinite programming with diagonal constraints. The approach, which we call the Mixing method, is extremely simple to implement, has no free parameters, and…
We propose a new technique that boosts the convergence of training generative adversarial networks. Generally, the rate of training deep models reduces severely after multiple iterations. A key reason for this phenomenon is that a deep…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
The Moving Sofa Problem, formally proposed by Leo Moser in 1966, seeks to determine the largest area of a two-dimensional shape that can navigate through an $L$-shaped corridor with unit width. The current best lower bound is about 2.2195,…
Hyperbolic Programming (HP) --minimizing a linear functional over an affine subspace of a finite-dimensional real vector space intersected with the so-called hyperbolicity cone-- is a class of convex optimization problems that contains…
Generalizing the simplex method, circuit augmentation schemes for linear programs follow circuit directions through the interior of the underlying polyhedron. Steepest-descent augmentation is especially promising, but an implementation of…
This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…
This paper presents a trajectory generation method that optimizes a quadratic cost functional with respect to linear system dynamics and to linear input and state constraints. The method is based on continuous-time flatness-based trajectory…
The recent impressive results of deep learning-based methods on computer vision applications brought fresh air to the research and industrial community. This success is mainly due to the process that allows those methods to learn…
For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering…
An algorithm and associated strategy for solving polynomial systems within the optimization framework is presented. The algorithm and strategy are named, respectively, the penetrating gradient algorithm and the deepest descent strategy. The…
A common way to manipulate heavy objects is to maintain at least one point of the object in contact with the environment during the manipulation. When the object has a cylindrical shape or, in general, a curved edge, not only sliding and…
Video processing solutions for motion analysis are key tasks in many computer vision applications, ranging from human activity recognition to object detection. In particular, speed estimation algorithms may be relevant in contexts such as…