T paper shows how many types of combinatorial problems can be embedded in continuous space and solved as nonconvex optimization problems. If the objective function and the constraints are linear, problems of this kind can be formulated as linear complementarity problems. An algorithm is presented to solve this type of problem and indicate its convergence properties. Computational comparisons ar...

A simple and uniied analysis is provided on the rate of local convergence for a class of high-order-infeasible-path-following algorithms for the P-linear complementarity problem (P-LCP). It is shown that the rate of local convergence of a-order algorithm with a centering step is + 1 if there is a strictly complementary solution and (+ 1)=2 otherwise. For the-order algorithm without the centerin...

A variational inequality problem (VIP) satisfying a constraint qual-iication can be reduced to a mixed complementarity problem (MCP). Monotonicity of the VIP implies that the MCP is also monotone. Introducing regularizing perturbations, a sequence of strictly monotone mixed complementarity problems is generated. It is shown that, if the original problem is solvable, the sequence of computable i...

We present a method to identify the parameters of a state space model for a max-plus-linear discrete event system from input-output sequences. The approach is based on recasting the identification problem as an optimization problem over the solution set of an extended linear complementarity problem. Recently, we have shown that such a problem can be solved much more efficiently than previously ...

We present an overview of our research on the use of generalized linear complementarity problems (LCPs) for analysis of continuously variable systems and discrete event systems. We indicate how the Generalized LCP can be used to analyze piecewise-linear resistive electrical circuits. Next we discuss how the Extended LCP can be used to solve some fundamental problems that arise in max-algebraic ...

this paper uses the l1−norm and the concept of the non-dominated vector, topropose a method to find a well-dispersed subset of non-dominated (wdsnd) vectorsof a multi-objective mixed integer linear programming (momilp) problem.the proposed method generalizes the proposed approach by tohidi and razavyan[tohidi g., s. razavyan (2014), determining a well-dispersed subset of non-dominatedvectors of...

We show that recently developed interior point methods for quadratic programming and linear complementarity problems can be put to use in solving discrete-time optimal control problems, with general pointwise constraints on states and controls. We describe interior point algorithms for a discrete time linear-quadratic regulator problem with mixed state/control constraints, and show how it can b...