Abstract: An optimal solution calculation device for an optimization problem includes an initial condition generation unit for generating an executable initial solution and an equality constraint set with respect to an optimization problem, an optimization calculation unit for calculating a solution of a simultaneous linear equation generated from an evaluation function and for calculating an evaluated solution that is a solution to minimize or maximize the evaluation function, and an update unit. A convergence determination unit of the optimization calculation unit determines that an iterative solution has converged when a residual norm is equal to or less than a convergence determination threshold value, and outputs the converged iterative solution as the evaluated solution. The update unit determines the evaluated solution as an optimal solution when an update of the equality constraint set is determined to be unnecessary, and the convergence determination threshold value is the first threshold value.

Abstract: To provide a traveling lane recognition apparatus and a traveling lane recognition method which can determine the reliability of the detected lane marking information in order to deal with the case where, even though the detecting state of the periphery monitoring apparatus is good, the reliability of the detected lane marking information is bad, and can set appropriately the lane marking information used for autonomous driving. A traveling lane recognition apparatus acquires detection lane marking information based on detection information of a periphery monitoring apparatus; acquires map lane marking information from map data; determines a reliability of the detection lane marking information based on variation of the detection lane marking information; and selects from the detection lane marking information and the map lane marking information based on the reliability, and calculates lane marking information for autonomous driving.

Abstract: A processor of a computing device comprises: a rearrangement unit to rearrange a plurality of elements included in each of a Hessian matrix of an evaluation function and a coefficient matrix of the linear constraint; a generation unit to generate a simultaneous linear equation for finding the optimal solution, based on the evaluation function including the rearranged Hessian matrix and the linear constraint including the rearranged coefficient matrix; and a search unit to find the optimal solution using the simultaneous linear equation. The rearrangement unit rearranges the plurality of elements so as to gather a sparse element of the plurality of elements included in the Hessian matrix, and rearranges the plurality of elements so as to gather a sparse element of the plurality of elements included in the coefficient matrix.

Abstract: A processor of a computing device comprises: a generation unit to generate an active constraint set based on an inequality constraint set and an initial solution; a search unit to find a solution of a simultaneous linear equation generated based on the active constraint set and an evaluation function; and an updating unit to update the active constraint set based on the solution obtained by the search unit. The generation unit adds, to the active constraint set, the first inequality constraint determined as being not linearly dependent on one or more second inequality constraints included in the active constraint set.