One of the most difficult parts of motion planning in configuration space is ensuring a trajectory does not collide with task-space obstacles in the environment. Generating regions that are convex and collision free i...
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K-means is a classical clustering algorithm with wide applications. However, soft K-means, or fuzzy c-means at m = 1, remains unsolved since 1981. To address this challenging open problem, we propose a novel clusterin...
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The paper is devoted to the implicit function theorem involving singular mappings. We also discuss the form of the tangent cone to the solution set of the generalized equations in singular case and give some examples ...
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Borsuk-Ulam’s theorem is a useful tool of algebraic topology. It states that for any continuous mapping f from the n-sphere to the n-dimensional Euclidean space, there exists a pair of antipodal points such that f(x)...
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This paper presents an integrated cross-resolution framework for the traffic system state identification (TSSI) problem by simultaneously considering traffic state estimation (TSE), traffic flow model parameter estima...
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This paper presents an integrated cross-resolution framework for the traffic system state identification (TSSI) problem by simultaneously considering traffic state estimation (TSE), traffic flow model parameter estimation (MPE), and queue profile estimation (QPE) on transportation networks using heterogeneous data sources. Systematically considering the three tasks, that is, TSE, MPE, and QPE, in an integrated modeling framework helps to fully utilize information from different components and takes advantage of larger solution spaces, which is expected to improve the reliability and accuracy of system identification results. However, potential inconsistencies between different modeling components are introduced at the same time and should be carefully dealt with to ensure model feasibility. To minimize such inconsistencies, a novel nonlinear programming model was developed to formulate the TSSI problem by considering traffic flow models and observations from different resolutions. At the macroscopic level, we used a fluid queue approximation to model the traffic system of interest. Based on the assumption of polynomial arrival and departure rates, critical system measures such as time-dependent delay, travel time, and queue length were analytically derived. At the mesoscopic level, with the adoption of continuous space-time distribution (CSTD) functions, a continuous traffic state representation scheme is introduced to model traffic flow variables such as traffic volume, speed, and density. CSTD functions maintain the differentiability of traffic state variables such that partial differential equations in traffic flow models can be comprehensively considered in the proposed framework. A computational graph is constructed to represent the nonlinear programming model in a sequential propagation structure, which is then solved using a forward-backward method. Extensive numerical experiments based on real-world and hypothetical datasets were designed to demonstrate the
In this paper we describe an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior point approach. The main theoretical results concern direction determination and step-length ...
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In this paper we describe an algorithm for solving nonlinear nonconvex programming problems, which is based on the interior point approach. The main theoretical results concern direction determination and step-length selection. We split inequality constraints into active and inactive parts to overcome problems with instability. Inactive constraints are eliminated directly, whereas active constraints are used for defining a symmetric indefinite linear system. Inexact solution of this system is obtained iteratively using indefinitely preconditioned conjugate gradient method. Theorems confirming efficiency of the indefinite preconditioner are introduced. Furthermore, a new merit function is defined and a filter principle is used for step-length selection. The algorithm was implemented in the interactive system for universal functional optimization UFO. Results of numerical experiments are reported.
This paper is devoted to the study of tilt stability in finite dimensional optimization via the approach of using the subgradient graphical derivative. We establish a new characterization of tilt-stable local minimize...
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In this paper, we study the following nonlinear nonconvex programming problem: ｛min/(x), ***{x) ≤ 0, i∈M, M = {1,2, …,m}. Under the condition that the feasible set is bounded and connected, and the feasible set ...
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In this paper, we study the following nonlinear nonconvex programming problem: ｛min/(x), ***{x) ≤ 0, i∈M, M = {1,2, …,m}. Under the condition that the feasible set is bounded and connected, and the feasible set does not satisfy the pseudo-normal cone conditions, we propose the combined homotopy method to solve this problem by constructing new constraint functions and a combined homotopy equation. The convergence of the method is proved and the existence of a smooth homotopy path from any interior point to a solution of the problem is established. Numerical examples show that this method is feasible and effective.
Four major approaches of nonlinear Goal programming are reviewed and discussed;(1) simplex based;(2) direct search;(3) gradient search and (4) interactive approaches. The applications of nonlinear Goal programming are...
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Four major approaches of nonlinear Goal programming are reviewed and discussed;(1) simplex based;(2) direct search;(3) gradient search and (4) interactive approaches. The applications of nonlinear Goal programming are also discussed and classified into the following nine areas: (1) engineering design;(2) energy;(3) manufacturing/metal cutting;(4) marketing;(5) finance and accounting;(6) agriculture/farm planning;(7) routing and scheduling;(8) quality control and (9) R&D project selection.
This paper considers the large-scale multiobjective nonlinear programming problem with block angular structure. A new method is proposed for deriving the compromising solution of the decisionmaker based on the fuzzy d...
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This paper considers the large-scale multiobjective nonlinear programming problem with block angular structure. A new method is proposed for deriving the compromising solution of the decisionmaker based on the fuzzy decision, considering the fuzzy goal of the decisionmaker for each objective function. The large-scale nonlinear programming problem (original problem) for deriving the solution based on the fuzzy decision is formulated. Then, based on the dual decomposition technique introduced by Lasdon, the dual problem for the original problem is formulated. A two-level optimization algorithm is proposed where the formulated dual problem is decomposed and the solution for the original problem is obtained by iteratively solving the subproblems. The validity of the algorithm is examined through a simple numerical example with the block angular structure.
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