Related papers: New sharp necessary optimality conditions for math…
We consider non-autonomous calculus of variations problems with a state constraint represented by a given closed set. We prove that if the interior of the Clarke tangent cone of the state constraint set is non-empty (this is the constraint…
This paper solves a new class of optimization problems under uncertainty, called Probable Event Constrained Optimization (PECO), which optimizes an objective function of decision variables and subjects to a set of Probable Event Constraints…
In this paper, we propose a a gradient-based neural network model to solve the mathematical programming problems with complementary constraints (MPCC). In order to facilitate tractable optimization, the problem MPCC is transformed via a…
In a Mathematical Program with Generalized Complementarity Constraints (MPGCC), complementarity relationships are imposed between each pair of variable blocks. MPGCC includes the traditional Mathematical Program with Complementarity…
Mathematical Program Networks (MPNs) are introduced in this work. An MPN is a collection of interdependent Mathematical Programs (MPs) which are to be solved simultaneously, while respecting the connectivity pattern of the network defining…
Various control schemes rely on a solution of a convex optimization problem involving a particular robust quadratic constraint, which can be reformulated as a linear matrix inequality using the well-known $\mathcal{S}$-lemma. However, the…
The paper suggests a new --- to the best of the author's knowledge --- characterization of decisions which are optimal in the multi-objective optimization problem with respect to a definite proper preference cone, a Euclidean cone with a…
We present new constraint qualification conditions for nonlinear semidefinite programming that extend some of the constant rank-type conditions from nonlinear programming. As an application of these conditions, we provide a unified global…
We consider the Mathematical Program with Complementarity Constraints (MPCC). One of the main challenges in solving this problem is the systematic failure of standard Constraint Qualifications (CQs). Carefully accounting for the…
We propose a novel approach to design a robust Model Predictive Controller (MPC) for constrained uncertain linear systems. The uncertain system is modeled as linear parameter varying with additive disturbance. Set bounds for the system…
In this work we are interested in nonlinear symmetric cone problems (NSCPs), which contain as special cases nonlinear semidefinite programming, nonlinear second order cone programming and the classical nonlinear programming problems. We…
Mathematical programs with complementarity constraints (MPCCs) are a challenging class of nonlinear optimization problems, because their nonlinear programming reformulations violate standard constraint qualifications at every feasible…
Quadratically constrained quadratic programs (QCQPs) are a highly expressive class of nonconvex optimization problems. While QCQPs are NP-hard in general, they admit a natural convex relaxation via the standard semidefinite program (SDP)…
Mathematical programs with vanishing constraints (MPVCs) are a class of nonlinear optimization problems with applications to various engineering problems such as truss topology design and robot motion planning. MPVCs are difficult problems…
This study explores B-stationarity of mathematical programs with complementarity constraints (MPCCs) and convergence behavior of MPCC algorithms. Special attention is given to the cases with biactive complementarity constraints. First, we…
In high-stakes engineering applications, optimization algorithms must come with provable worst-case guarantees over a mathematically defined class of problems. Designing for the worst case, however, inevitably sacrifices performance on the…
In this paper, we clarify a serious misinterpretation and consequent misuse of the Principle of Maximum Conformality (PMC), which also can be served as a mini review of PMC. We emphasize that the purpose of the PMC is to achieve precise…
Based on the tools of limiting variational analysis, we derive a sequential necessary optimality condition for nonsmooth mathematical programs which holds without any additional assumptions. In order to ensure that stationary points in this…
The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved non convex…
A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is…