This paper deals with bilevel programming programs with convex lower level problems. New necessary and sufficient optimality conditions that involve a single-level mathematical program satisfying the linear independence constraint qualification are introduced. These conditions are solved by an interior point technique for nonlinear programming. Neither the optimality conditions nor the algorith...

We develop a method for computing policies in Markov decision processes with risk-sensitive measures subject to temporal logic constraints. Specifically, we use a particular risk-sensitive measure from cumulative prospect theory, which has been previously adopted in psychology and economics. The nonlinear transformation of the probabilities and utility functions yields a nonlinear programming p...

In this work, we present a new hybrid algorithm for convex Mixed Integer Nonlinear Programming combining branch-and-bound and outer approximation algorithms in an e ective and e cient way.

We show that evolutionarily stable states in general (nonlinear) population games (which can be viewed as continuous vector fields constrained on a polytope) are asymptotically stable under a multiplicative weights dynamic (under appropriate choices of a parameter called the learning rate or step size, which we demonstrate to be crucial to achieve convergence, as otherwise even chaotic behavior...

In the context of a variation of the standard UFL (Uncapacitated Facility Location) problem, but with an objective function that is a separable convex quadratic function of the transportation costs, we present some techniques for improving relaxations of MINLP formulations. We use a disaggregation principal and a strategy of developing model-specific valid inequalities (some nonlinear), which e...

By using the the equivalent expression of the second order cone, we reformulate the convex second order cone programming as a boxed constrained optimization, which is a nonlinear programming with four nonnegative constraints. We give the conditions under which the stationary point of the reformulation problem solve the original problem.

We introduce the concept of sos-convex Lyapunov functions for stability analysis of discrete time switched systems. These are polynomial Lyapunov functions that have an algebraic certificate of convexity, and can be efficiently found by semidefinite programming. We show that sos-convex Lyapunov functions are universal (i.e., necessary and sufficient) for stability analysis of switched linear sy...

A kind of generalized convex set, called as local star-shaped E-invex set with respect to η, is presented, and some of its important characterizations are derived. Based on this concept, a new class of functions, named as semilocal E-preinvex functions, which is a generalization of semi-Epreinvex functions and semilocal E-convex functions, is introduced. Simultaneously, some of its basic proper...

We present a homogeneous algorithm equipped with a modified potential function for the monotone complementarity problem. We show that this potential function is reduced by at least a constant amount if a scaled Lipschitz condition is satisfied. A practical algorithm based on this potential function is implemented in a software package named iOptimize. The implementation in iOptimize maintains g...