Estimation of time-varying regression model constrained at each time moment by linear inequalities is a natural statistical formulation of a wide class of nonstationary signal processing problems. The presence of linear constraints turns the originally quadratic three-diagonal problem of minimizing the residual squares sum, which is solvable by the linear Kalman-Bucy filtration-smoothing proced...

This paper describes a technique for generating disjointly constrained bilinear programming test problems with known solutions and properties. The proposed construction technique applies a simple random tranformation of variables to a separable bilinear programming problem that is constructed by combining disjoint low-dimensional bilinear programs.

This paper is devoted to sequential decision problems with imprecise probabilities. We study the problem of determining an optimal strategy according to the Hurwicz criterion in decision trees. More precisely, we investigate this problem from the computational viewpoint. When the decision tree is separable (to be defined in the paper), we provide an operational approach to compute an optimal st...

Abstract In this paper, we present an inexact multiblock alternating direction method for the point-contact friction model of force-optimization problem (FOP). The friction-cone constraints FOP are reformulated as Cartesian product circular cones. We focus on convex quadratic circular-cone programming FOP, which is exact cone-programming model. Coupled with separable objective function, recast ...

We study a generic minimization problem with separable non-convex piecewise linear costs, showing that the linear programming (LP) relaxation of three textbook mixed-integer programming formulations each approximates the cost function by its lower convex envelope. We also show a relationship between this result and classical Lagrangian duality theory.

Geometric programming problem is a powerful tool for solving some special type non-linear programming problems. It has a wide range of applications in optimization and engineering for solving some complex optimization problems. Many applications of geometric programming are on engineering design problems where parameters are estimated using geometric programming. When the parameters in the prob...

An exact semidefinite linear programming (SDP) relaxation of a nonlinear semidefinite programming problem is a highly desirable feature because a semidefinite linear programming problem can efficiently be solved. This paper addresses the basic issue of which nonlinear semidefinite programming problems possess exact SDP relaxations under a constraint qualification. We do this by establishing exa...