This paper reviews the development of dierent versions of nonlinear conjugate gradient methods, with special attention given to global convergence properties.

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A survey of nonlinear conjugate gradient methods

We consider large margin estimation in a broad range of prediction models where inference involves solving combinatorial optimization problems, for example, weighted graph-cuts or matchings. Our goal is to learn parameters such that inference using the model reproduces correct answers on the training data. Our method relies on the expressive power of convex optimization problems to compactly capture inference or solution optimality in structured prediction models. Directly embedding this structure within the learning formulation produces concise convex problems for efficient estimation of very complex and diverse models. We describe experimental results on a matching task, disulfide connectivity prediction, showing significant improvements over state-of-the-art methods.

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Learning structured prediction models: a large margin approach

Some developments in general variational inequalities

In this paper, we study inverse optimization problems defined as follows. LetS denote the set of feasible solutions of an optimization problemP, letc be a specified cost vector, andx0 be a given feasible solution. The solutionx0 may or may not be an optimal solution ofP with respect to the cost vectorc. The inverse optimization problem is to perturb the cost vectorc tod so thatx0 is an optimal solution ofP with respect tod and ||d- c || p is minimum, where ||d- c || p is some selectedLp norm. In this paper, we consider the inverse linear programming problem underL1 norm (where ||d- c || p= ? j?Jw j|d j-c j|, withJ denoting the index set of variablesx jandw jdenoting the weight of the variablej) and underL8 norm (where||d- c || p= max j?J{w j|d j-c j|} ). We prove the following results: (i) If the problemP is a linear programming problem, then its inverse problem under theL1 as well asL8 norm is also a linear programming problem. (ii) If the problemP is a shortest path, assignment or minimum cut problem, then its inverse problem under theL1 norm and unit weights can be solved by solving a problem of the same kind. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flow problem. (iii) If the problemP is a minimum cost flow problem, then its inverse problem under theL1 norm and unit weights reduces to solving a unit-capacity minimum cost flow problem. For the nonunit weight case, the inverse problem reduces to solving a minimum cost flow problem. (iv) If the problemP is a minimum cost flow problem, then its inverse problem under theL8 norm and unit weights reduces to solving a minimum mean cycle problem. For the nonunit weight case, the inverse problem reduces to solving a minimum cost-to-time ratio cycle problem. (v) If the problemP is polynomially solvable for linear cost functions, then inverse versions ofP under theL1 andL8 norms are also polynomially solvable.

Inverse Optimization

In this bibliography main directions of research as well as main fields of applications of bilevel programming problems and mathematical programs with equilibrium constraints are summarized. Focus is also on the difficulties arising from nonuniqueness of lower-level optimal solutions and on optimality conditions.

Jianzhong Zhang

Papers

An inverse DEA model for inputs/outputs estimate

Properties and numerical performance of quasi-Newton methods with modified quasi-Newton equations

Calculating some inverse linear programming problems

Some recent advances in projection-type methods for variational inequalities

Inverse median problems